메뉴 건너뛰기




Volumn 5, Issue , 1997, Pages 3-207

Numerical path following

Author keywords

[No Author keywords available]

Indexed keywords


EID: 70350662980     PISSN: 15708659     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-8659(97)80002-6     Document Type: Review
Times cited : (168)

References (433)
  • 2
    • 0000110392 scopus 로고
    • An implementation of Karmarkar's algorithm for linear programming
    • Adler I., Resende G.C., Veiga G., and Karmarkar N. An implementation of Karmarkar's algorithm for linear programming. Math. Programming 44 (1989) 297-335
    • (1989) Math. Programming , vol.44 , pp. 297-335
    • Adler, I.1    Resende, G.C.2    Veiga, G.3    Karmarkar, N.4
  • 3
    • 0023287948 scopus 로고
    • Average intersection and pivoting densities
    • Alexander J.C. Average intersection and pivoting densities. SIAM J. Numer. Anal. 24 (1987) 129-146
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 129-146
    • Alexander, J.C.1
  • 4
    • 33646992979 scopus 로고
    • Global convergence rates of piecewise-linear continuation methods: A probabilistic approach
    • Eaves B.C., Gould F.J., Peitgen H.-O., and Todd M.J. (Eds), Plenum Press, New York
    • Alexander J.C., and Slud E.V. Global convergence rates of piecewise-linear continuation methods: A probabilistic approach. In: Eaves B.C., Gould F.J., Peitgen H.-O., and Todd M.J. (Eds). Homotopy Methods and Global Convergence (1983), Plenum Press, New York 15-30
    • (1983) Homotopy Methods and Global Convergence , pp. 15-30
    • Alexander, J.C.1    Slud, E.V.2
  • 5
    • 33646990969 scopus 로고
    • Bifurcations arising in the calculation of critical points via homotopy methods
    • Numerical Methods for Bifurcation Problems. Küpper T., Mittelmann H.D., and Weber H. (Eds), Birkhäuser, New York
    • Allgower E.L. Bifurcations arising in the calculation of critical points via homotopy methods. In: Küpper T., Mittelmann H.D., and Weber H. (Eds). Numerical Methods for Bifurcation Problems. ISNM 70 (1984), Birkhäuser, New York 15-28
    • (1984) ISNM , vol.70 , pp. 15-28
    • Allgower, E.L.1
  • 7
    • 70350694378 scopus 로고
    • Allgower E.L., Böhmer K., and Golubitsky M. (Eds), Birkhäuser, Basel
    • In: Allgower E.L., Böhmer K., and Golubitsky M. (Eds). Bifurcation and Symmetry. ISNM 104 (1992), Birkhäuser, Basel
    • (1992) ISNM , vol.104
  • 8
    • 0039656936 scopus 로고
    • A complete bifurcation scenario for the 2-D nonlinear Laplacian with Neumann boundary conditions
    • Bifurcation and Chaos: Analysis, Algorithms, Applications. Seydel R., Schneider F.W., Küpper T., and Troger H. (Eds), Birkhäuser, Basel
    • Allgower E.L., Böhmer K., and Mei Z. A complete bifurcation scenario for the 2-D nonlinear Laplacian with Neumann boundary conditions. In: Seydel R., Schneider F.W., Küpper T., and Troger H. (Eds). Bifurcation and Chaos: Analysis, Algorithms, Applications. ISNM 97 (1991), Birkhäuser, Basel 1-18
    • (1991) ISNM , vol.97 , pp. 1-18
    • Allgower, E.L.1    Böhmer, K.2    Mei, Z.3
  • 9
    • 0039835037 scopus 로고
    • On a problem decomposition for semi-linear nearly symmetric elliptic problems
    • Parallel Algorithms for PDE's. Hackbusch W. (Ed), Vieweg Verlag, Basel
    • Allgower E.L., Böhmer K., and Mei Z. On a problem decomposition for semi-linear nearly symmetric elliptic problems. In: Hackbusch W. (Ed). Parallel Algorithms for PDE's. Notes on Numerical Fluid Mechanics 31 (1991), Vieweg Verlag, Basel 1-17
    • (1991) Notes on Numerical Fluid Mechanics , vol.31 , pp. 1-17
    • Allgower, E.L.1    Böhmer, K.2    Mei, Z.3
  • 10
    • 0009459750 scopus 로고
    • On new bifurcation results for semi-linear elliptic equations with symmetries
    • Whiteman J. (Ed), Academic Press, Braunschweig
    • Allgower E.L., Böhmer K., and Mei Z. On new bifurcation results for semi-linear elliptic equations with symmetries. In: Whiteman J. (Ed). The Mathematics of Finite Elements and Applications VII (1991), Academic Press, Braunschweig 487-494
    • (1991) The Mathematics of Finite Elements and Applications , vol.VII , pp. 487-494
    • Allgower, E.L.1    Böhmer, K.2    Mei, Z.3
  • 11
    • 0001447616 scopus 로고
    • Continuation and local perturbation for multiple bifurcations
    • Allgower E.L., and Chien C.-S. Continuation and local perturbation for multiple bifurcations. SIAM J. Sci. Statist. Comput. 7 (1986) 1265-1281
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 1265-1281
    • Allgower, E.L.1    Chien, C.-S.2
  • 15
    • 0141903558 scopus 로고
    • Generation of triangulations by reflections
    • Allgower E.L., and Georg K. Generation of triangulations by reflections. Utilitas Math. 16 (1979) 123-129
    • (1979) Utilitas Math. , vol.16 , pp. 123-129
    • Allgower, E.L.1    Georg, K.2
  • 16
    • 0040848850 scopus 로고
    • Homotopy methods for approximating several solutions to nonlinear systems of equations
    • Forster W. (Ed), North-Holland, Brunel
    • Allgower E.L., and Georg K. Homotopy methods for approximating several solutions to nonlinear systems of equations. In: Forster W. (Ed). Numerical Solution of Highly Nonlinear Problems (1980), North-Holland, Brunel 253-270
    • (1980) Numerical Solution of Highly Nonlinear Problems , pp. 253-270
    • Allgower, E.L.1    Georg, K.2
  • 17
    • 0011286603 scopus 로고
    • Predictor-corrector and simplicial methods for approximating fixed points and zero points of nonlinear mappings
    • Bachem A., Grötschel M., and Korte B. (Eds), Springer, Amsterdam
    • Allgower E.L., and Georg K. Predictor-corrector and simplicial methods for approximating fixed points and zero points of nonlinear mappings. In: Bachem A., Grötschel M., and Korte B. (Eds). Mathematical Programming: The State of the Art (1983), Springer, Amsterdam 15-56
    • (1983) Mathematical Programming: The State of the Art , pp. 15-56
    • Allgower, E.L.1    Georg, K.2
  • 18
    • 0013629924 scopus 로고
    • Relationships between deflation and global methods in the problem of approximating additional zeros of a system of nonlinear equations
    • Eaves B.C., Gould F.J., Peitgen H.-O., and Todd M.J. (Eds), Plenum Press, Berlin
    • Allgower E.L., and Georg K. Relationships between deflation and global methods in the problem of approximating additional zeros of a system of nonlinear equations. In: Eaves B.C., Gould F.J., Peitgen H.-O., and Todd M.J. (Eds). Homotopy Methods and Global Convergence (1983), Plenum Press, Berlin 31-42
    • (1983) Homotopy Methods and Global Convergence , pp. 31-42
    • Allgower, E.L.1    Georg, K.2
  • 19
    • 12444345572 scopus 로고
    • Estimates for piecewise linear approximations of implicitly defined manifolds
    • Allgower E.L., and Georg K. Estimates for piecewise linear approximations of implicitly defined manifolds. Appl. Math. Lett. 1 5 (1989) 1-7
    • (1989) Appl. Math. Lett. , vol.1 , Issue.5 , pp. 1-7
    • Allgower, E.L.1    Georg, K.2
  • 20
    • 0001128796 scopus 로고
    • Numerical Continuation Methods: An Introduction
    • Springer, New York
    • Allgower E.L., and Georg K. Numerical Continuation Methods: An Introduction. Series in Computational Mathematics 13 (1990), Springer, New York 388
    • (1990) Series in Computational Mathematics , vol.13 , pp. 388
    • Allgower, E.L.1    Georg, K.2
  • 21
    • 84971957489 scopus 로고
    • Continuation and path following
    • Allgower E.L., and Georg K. Continuation and path following. Acta Numer. 2 (1993) 1-64
    • (1993) Acta Numer. , vol.2 , pp. 1-64
    • Allgower, E.L.1    Georg, K.2
  • 23
    • 0009452676 scopus 로고
    • Exploiting permutation symmetry with fixed points in linear equations
    • Exploiting Symmetry in Applied and Numerical Analysis. Allgower E.L., Georg K., and Miranda R. (Eds), American Mathematical Society, Berlin
    • Allgower E.L., Georg K., and Miranda R. Exploiting permutation symmetry with fixed points in linear equations. In: Allgower E.L., Georg K., and Miranda R. (Eds). Exploiting Symmetry in Applied and Numerical Analysis. Lectures in Applied Mathematics 29 (1993), American Mathematical Society, Berlin 23-36
    • (1993) Lectures in Applied Mathematics , vol.29 , pp. 23-36
    • Allgower, E.L.1    Georg, K.2    Miranda, R.3
  • 24
    • 0041309101 scopus 로고
    • Exploiting symmetry in 3D boundary element methods
    • Contributions in Numerical Mathematics. Agarwal R.P. (Ed), World Scientific, Providence, RI
    • Allgower E.L., Georg K., and Walker J. Exploiting symmetry in 3D boundary element methods. In: Agarwal R.P. (Ed). Contributions in Numerical Mathematics. World Scientific Series in Applicable Analysis 2 (1993), World Scientific, Providence, RI 15-25
    • (1993) World Scientific Series in Applicable Analysis , vol.2 , pp. 15-25
    • Allgower, E.L.1    Georg, K.2    Walker, J.3
  • 25
    • 0023329383 scopus 로고
    • An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces
    • Allgower E.L., and Gnutzmann S. An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces. SIAM J. Numer. Anal. 24 (1987) 452-469
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 452-469
    • Allgower, E.L.1    Gnutzmann, S.2
  • 26
    • 0026240956 scopus 로고
    • Simplicial pivoting for mesh generation of implicitly defined surfaces
    • Allgower E.L., and Gnutzmann S. Simplicial pivoting for mesh generation of implicitly defined surfaces. Comput. Aided Geom. Design 8 (1991) 305-325
    • (1991) Comput. Aided Geom. Design , vol.8 , pp. 305-325
    • Allgower, E.L.1    Gnutzmann, S.2
  • 27
    • 0022048415 scopus 로고
    • An algorithm for piecewise-linear approximation of an implicitly defined manifold
    • Allgower E.L., and Schmidt P.H. An algorithm for piecewise-linear approximation of an implicitly defined manifold. SIAM J. Numer. Anal. 22 (1985) 322-346
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 322-346
    • Allgower, E.L.1    Schmidt, P.H.2
  • 29
    • 12344324485 scopus 로고
    • The granularity of parallel homotopy algorithms for polynomial systems of equations
    • Allison D.C.S., Harimoto S., and Watson L.T. The granularity of parallel homotopy algorithms for polynomial systems of equations. Intern. J. Comput. Math. 29 (1989) 21-37
    • (1989) Intern. J. Comput. Math. , vol.29 , pp. 21-37
    • Allison, D.C.S.1    Harimoto, S.2    Watson, L.T.3
  • 30
    • 0017014016 scopus 로고
    • Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces
    • Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976) 620-709
    • (1976) SIAM Rev. , vol.18 , pp. 620-709
    • Amann, H.1
  • 31
    • 2642577359 scopus 로고
    • Positive solutions of asymptotically linear elliptic eigenvalue problems
    • Ambrosetti A., and Hess P. Positive solutions of asymptotically linear elliptic eigenvalue problems. J. Math. Anal. Appl. 73 (1980) 411-422
    • (1980) J. Math. Anal. Appl. , vol.73 , pp. 411-422
    • Ambrosetti, A.1    Hess, P.2
  • 32
    • 0008162092 scopus 로고
    • User's Guide to a boundary element package for solving integral equations on piecewise smooth surfaces
    • Univ. of Iowa, Singapore
    • Atkinson K.E. User's Guide to a boundary element package for solving integral equations on piecewise smooth surfaces. Report 44 (1993), Univ. of Iowa, Singapore
    • (1993) Report 44
    • Atkinson, K.E.1
  • 34
    • 0019540531 scopus 로고
    • Application of the representation theory of finite groups to field computation problems with symmetrical boundaries
    • Ballisti R., Hafner C., and Leuchtman P. Application of the representation theory of finite groups to field computation problems with symmetrical boundaries. IEEE Trans. Magnetics 18 (1982) 584-587
    • (1982) IEEE Trans. Magnetics , vol.18 , pp. 584-587
    • Ballisti, R.1    Hafner, C.2    Leuchtman, P.3
  • 35
    • 84935919745 scopus 로고
    • Panel method in fluid mechanics with emphasis on aerodynamics
    • Hackbusch W. (Ed), Vieweg
    • Ballman J., Eppler R., and Hackbusch W. Panel method in fluid mechanics with emphasis on aerodynamics. In: Hackbusch W. (Ed). Notes on Numerical Fluid Dynamics 21 (1988), Vieweg
    • (1988) Notes on Numerical Fluid Dynamics , vol.21
    • Ballman, J.1    Eppler, R.2    Hackbusch, W.3
  • 36
    • 0000159210 scopus 로고
    • PLTMGC: A multi-grid continuation program for parameterized non-linear elliptic systems
    • Bank R.E., and Chan T.F. PLTMGC: A multi-grid continuation program for parameterized non-linear elliptic systems. SIAM J. Sci. Statist. Comput. 7 (1986) 540-559
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 540-559
    • Bank, R.E.1    Chan, T.F.2
  • 38
    • 84966258893 scopus 로고
    • The nonlinear geometry of linear programming, I: Affine and projective scaling trajectories, II: Legendre transform coordinates and central trajectories
    • Bayer D., and Lagarias J.C. The nonlinear geometry of linear programming, I: Affine and projective scaling trajectories, II: Legendre transform coordinates and central trajectories. Trans. Amer. Math. Soc. 314 (1989) 499-581
    • (1989) Trans. Amer. Math. Soc. , vol.314 , pp. 499-581
    • Bayer, D.1    Lagarias, J.C.2
  • 40
    • 34250406508 scopus 로고
    • The number of roots of a system of equations
    • Bernstein D.N. The number of roots of a system of equations. Functional Anal. Appl. 9 (1975) 1-4
    • (1975) Functional Anal. Appl. , vol.9 , pp. 1-4
    • Bernstein, D.N.1
  • 41
    • 0002098825 scopus 로고
    • Sur la généralisation du problème de Dirichlet
    • Bernstein S. Sur la généralisation du problème de Dirichlet. Math. Ann. 69 (1910) 82-136
    • (1910) Math. Ann. , vol.69 , pp. 82-136
    • Bernstein, S.1
  • 44
    • 0040867941 scopus 로고
    • Very large-scale linear programming: A case study in combining interior point and simplex methods
    • Rutgers Univ., Germany
    • Bixby R.E., Gregory J.W., Lustig I.J., Marsten R.E., and Shanno D.F. Very large-scale linear programming: A case study in combining interior point and simplex methods. Technical Report RRR 34-91 (1991), Rutgers Univ., Germany
    • (1991) Technical Report RRR 34-91
    • Bixby, R.E.1    Gregory, J.W.2    Lustig, I.J.3    Marsten, R.E.4    Shanno, D.F.5
  • 45
    • 0001030418 scopus 로고
    • A multigrid continuation method for elliptic problems with folds
    • Bolstad J.H., and Keller H.B. A multigrid continuation method for elliptic problems with folds. SIAM J. Sci. Statist. Comput. 7 (1986) 1081-1104
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 1081-1104
    • Bolstad, J.H.1    Keller, H.B.2
  • 46
    • 0022733505 scopus 로고
    • Symmetry, groups, and boundary value problems. A progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry
    • Bossavit A. Symmetry, groups, and boundary value problems. A progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry. Comput. Methods Appl. Mech. Engrg. 56 (1986) 167-215
    • (1986) Comput. Methods Appl. Mech. Engrg. , vol.56 , pp. 167-215
    • Bossavit, A.1
  • 47
    • 0027683194 scopus 로고
    • Boundary value problems with symmetry and their approximation by finite elements
    • Bossavit A. Boundary value problems with symmetry and their approximation by finite elements. SIAM J. Appl. Math. 53 (1993) 1352-1380
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 1352-1380
    • Bossavit, A.1
  • 48
    • 0025508858 scopus 로고
    • Least-change secant updates of nonsquare matrices
    • Bourji S.K., and Walker H.F. Least-change secant updates of nonsquare matrices. SIAM J. Numer. Math. 27 (1990) 1263-1294
    • (1990) SIAM J. Numer. Math. , vol.27 , pp. 1263-1294
    • Bourji, S.K.1    Walker, H.F.2
  • 49
    • 0000137128 scopus 로고
    • Widely convergent method for finding multiple solutions of simultaneous nonlinear equations
    • Branin F.H. Widely convergent method for finding multiple solutions of simultaneous nonlinear equations. IBM J. Res. Develop. 16 (1972) 504-522
    • (1972) IBM J. Res. Develop. , vol.16 , pp. 504-522
    • Branin, F.H.1
  • 50
    • 0000264010 scopus 로고
    • A method for finding multiple extrema of a function of n variables
    • Lootsma F.A. (Ed), Academic Press, New Brunswick, NJ
    • Branin F.H., and Hoo S.K. A method for finding multiple extrema of a function of n variables. In: Lootsma F.A. (Ed). Numerical Methods for Non-Linear Optimization (1972), Academic Press, New Brunswick, NJ 231-237
    • (1972) Numerical Methods for Non-Linear Optimization , pp. 231-237
    • Branin, F.H.1    Hoo, S.K.2
  • 51
    • 0002435262 scopus 로고
    • Finite dimensional approximation of nonlinear problems. Part 1: Branches of nonsingular solutions
    • Brezzi F., Rappaz J., and Raviart P.A. Finite dimensional approximation of nonlinear problems. Part 1: Branches of nonsingular solutions. Numer. Math. 36 (1980) 1-25
    • (1980) Numer. Math. , vol.36 , pp. 1-25
    • Brezzi, F.1    Rappaz, J.2    Raviart, P.A.3
  • 52
    • 34250245747 scopus 로고
    • Finite dimensional approximation of nonlinear problems. Part 2: Limit points
    • Brezzi F., Rappaz J., and Raviart P.A. Finite dimensional approximation of nonlinear problems. Part 2: Limit points. Numer. Math. 37 (1980) 1-28
    • (1980) Numer. Math. , vol.37 , pp. 1-28
    • Brezzi, F.1    Rappaz, J.2    Raviart, P.A.3
  • 53
    • 34250231891 scopus 로고
    • Finite dimensional approximation of nonlinear problems. Part 3: Simple bifurcation points
    • Brezzi F., Rappaz J., and Raviart P.A. Finite dimensional approximation of nonlinear problems. Part 3: Simple bifurcation points. Numer. Math. 38 (1981) 1-30
    • (1981) Numer. Math. , vol.38 , pp. 1-30
    • Brezzi, F.1    Rappaz, J.2    Raviart, P.A.3
  • 55
    • 33646991054 scopus 로고
    • Infinite retrogression in the Eaves-Saigal algorithm
    • Brooks P.S. Infinite retrogression in the Eaves-Saigal algorithm. Math. Programming 19 (1980) 313-327
    • (1980) Math. Programming , vol.19 , pp. 313-327
    • Brooks, P.S.1
  • 56
    • 34250967150 scopus 로고
    • Über Abbildung von Mannigfaltigkeiten
    • Brouwer L.E.J. Über Abbildung von Mannigfaltigkeiten. Math. Ann. 71 (1912) 97-115
    • (1912) Math. Ann. , vol.71 , pp. 97-115
    • Brouwer, L.E.J.1
  • 57
    • 0009632194 scopus 로고
    • Deflation techniques for the calculation of further solutions of a nonlinear system
    • Brown K.M., and Gearhart W.B. Deflation techniques for the calculation of further solutions of a nonlinear system. Numer. Math. 16 (1971) 334-342
    • (1971) Numer. Math. , vol.16 , pp. 334-342
    • Brown, K.M.1    Gearhart, W.B.2
  • 58
    • 84968510937 scopus 로고
    • A class of methods for solving nonlinear simultaneous equations
    • Broyden C.G. A class of methods for solving nonlinear simultaneous equations. Math. Comp. 19 (1965) 577-593
    • (1965) Math. Comp. , vol.19 , pp. 577-593
    • Broyden, C.G.1
  • 59
    • 0022213743 scopus 로고
    • Distillation calculations using a locally parametrized continuation method
    • Byrne G.D., and Baird L.A. Distillation calculations using a locally parametrized continuation method. Comput. Chem. Engrg. 9 (1985) 593-599
    • (1985) Comput. Chem. Engrg. , vol.9 , pp. 593-599
    • Byrne, G.D.1    Baird, L.A.2
  • 60
    • 84968511777 scopus 로고
    • An optimal condition for determining the exact number of roots of a polynomial system
    • Bonn, Germany
    • Canny J., and Rojas J.M. An optimal condition for determining the exact number of roots of a polynomial system. Proceedings of the ISSAC 91. Bonn, Germany (1991) 96-102
    • (1991) Proceedings of the ISSAC 91 , pp. 96-102
    • Canny, J.1    Rojas, J.M.2
  • 61
    • 0040463516 scopus 로고
    • An interior point method for quadratic programs based on conjugate projected gradients
    • Rutgers Univ.
    • Carpenter T.J., and Shanno D.F. An interior point method for quadratic programs based on conjugate projected gradients. Technical Report RRR 55-91 (1991), Rutgers Univ.
    • (1991) Technical Report RRR 55-91
    • Carpenter, T.J.1    Shanno, D.F.2
  • 62
    • 0001276330 scopus 로고
    • Deflation techniques and block-elimination algorithms for solving bordered singular systems
    • Chan T.F. Deflation techniques and block-elimination algorithms for solving bordered singular systems. SIAM J. Sci. Stat. Comp. 5 (1984) 121-134
    • (1984) SIAM J. Sci. Stat. Comp. , vol.5 , pp. 121-134
    • Chan, T.F.1
  • 63
    • 0000873548 scopus 로고
    • Newton-like pseudo-arclength methods for computing simple turning points
    • Chan T.F. Newton-like pseudo-arclength methods for computing simple turning points. SIAM J. Sci. Statist. Comput. 5 (1984) 135-148
    • (1984) SIAM J. Sci. Statist. Comput. , vol.5 , pp. 135-148
    • Chan, T.F.1
  • 64
    • 0039050372 scopus 로고
    • Techniques for large sparse systems arising from continuation methods
    • Numerical Methods for Bifurcation Problems. Küpper T., Mittelmann H.D., and Weber H. (Eds), Birkhäuser, New Brunswick, NJ
    • Chan T.F. Techniques for large sparse systems arising from continuation methods. In: Küpper T., Mittelmann H.D., and Weber H. (Eds). Numerical Methods for Bifurcation Problems. ISNM 70 (1984), Birkhäuser, New Brunswick, NJ 116-128
    • (1984) ISNM , vol.70 , pp. 116-128
    • Chan, T.F.1
  • 65
    • 0005457259 scopus 로고
    • Arc-length continuation and multi-grid techniques for nonlinear eigenvalue problems
    • Chan T.F., and Keller H.B. Arc-length continuation and multi-grid techniques for nonlinear eigenvalue problems. SIAM J. Sci. Statist. Comput. 3 (1982) 173-194
    • (1982) SIAM J. Sci. Statist. Comput. , vol.3 , pp. 173-194
    • Chan, T.F.1    Keller, H.B.2
  • 66
    • 0141937375 scopus 로고
    • Iterative methods for solving bordered systems with applications to continuation methods
    • Chan T.F., and Saad Y. Iterative methods for solving bordered systems with applications to continuation methods. SIAM J. Sci. Statist. Comput. 6 (1985) 438-451
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 438-451
    • Chan, T.F.1    Saad, Y.2
  • 67
    • 0017525650 scopus 로고
    • Continuation methods in circuit analysis
    • Chao K.S., and Saeks R. Continuation methods in circuit analysis. Proc. IEEE 65 (1977) 1187-1194
    • (1977) Proc. IEEE , vol.65 , pp. 1187-1194
    • Chao, K.S.1    Saeks, R.2
  • 68
    • 0022806584 scopus 로고
    • Multiple steady state solutions for interlinked separation systems
    • Chavez R., Seader J.D., and Wayburn T.L. Multiple steady state solutions for interlinked separation systems. Ind. Eng. Chem. Fundam. 25 (1986) 566-576
    • (1986) Ind. Eng. Chem. Fundam. , vol.25 , pp. 566-576
    • Chavez, R.1    Seader, J.D.2    Wayburn, T.L.3
  • 69
    • 0024662374 scopus 로고
    • Secondary bifurcations in the buckling problem
    • Chien C.-S. Secondary bifurcations in the buckling problem. J. Comput. Appl. Math. 25 (1989) 277-287
    • (1989) J. Comput. Appl. Math. , vol.25 , pp. 277-287
    • Chien, C.-S.1
  • 71
    • 84966216764 scopus 로고
    • Finding zeros of maps: Homotopy methods that are constructive with probability one
    • Chow S.N., Mallet-Paret J., and Yorke J.A. Finding zeros of maps: Homotopy methods that are constructive with probability one. Math. Comp. 32 (1978) 887-899
    • (1978) Math. Comp. , vol.32 , pp. 887-899
    • Chow, S.N.1    Mallet-Paret, J.2    Yorke, J.A.3
  • 72
    • 33646990740 scopus 로고
    • A homotopy method for locating all zeros of a system of polynomials
    • Functional Differential Equations and Approximation of Fixed Points. Peitgen H.-O., and Walther H.-O. (Eds), Springer, New York
    • Chow S.N., Mallet-Paret J., and Yorke J.A. A homotopy method for locating all zeros of a system of polynomials. In: Peitgen H.-O., and Walther H.-O. (Eds). Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Math. 730 (1979), Springer, New York 77-88
    • (1979) Lecture Notes in Math. , vol.730 , pp. 77-88
    • Chow, S.N.1    Mallet-Paret, J.2    Yorke, J.A.3
  • 73
    • 0028416213 scopus 로고
    • Matrices with rank deficiency two in eigenvalue problems and dynamical systems
    • Chu K.-W.E., Govaerts W., and Spence A. Matrices with rank deficiency two in eigenvalue problems and dynamical systems. SIAM J. Num. Anal. 31 (1994) 524-539
    • (1994) SIAM J. Num. Anal. , vol.31 , pp. 524-539
    • Chu, K.-W.E.1    Govaerts, W.2    Spence, A.3
  • 74
    • 0040830341 scopus 로고
    • The generalized Toda flow, the QR algorithm and the center manifold theory
    • Chu M.T. The generalized Toda flow, the QR algorithm and the center manifold theory. SIAM J. Alg. Disc. Meth. 5 (1984) 187-201
    • (1984) SIAM J. Alg. Disc. Meth. , vol.5 , pp. 187-201
    • Chu, M.T.1
  • 75
    • 0001806232 scopus 로고
    • A simple application of the homotopy method to symmetric eigenvalue problems
    • Chu M.T. A simple application of the homotopy method to symmetric eigenvalue problems. Linear Algebra Appl. 59 (1984) 85-90
    • (1984) Linear Algebra Appl. , vol.59 , pp. 85-90
    • Chu, M.T.1
  • 76
    • 0038953719 scopus 로고
    • A continuous approximation to the generalized Schur's decomposition
    • Chu M.T. A continuous approximation to the generalized Schur's decomposition. Linear Algebra Appl. 78 (1986) 119-132
    • (1986) Linear Algebra Appl. , vol.78 , pp. 119-132
    • Chu, M.T.1
  • 77
    • 0024073497 scopus 로고
    • On the continuous realization of iterative processes
    • Chu M.T. On the continuous realization of iterative processes. SIAM Rev. 30 (1988) 375-387
    • (1988) SIAM Rev. , vol.30 , pp. 375-387
    • Chu, M.T.1
  • 78
    • 0039206135 scopus 로고
    • Solving additive inverse eigenvalue problems for symmetric matrices by the homotopy method
    • Chu M.T. Solving additive inverse eigenvalue problems for symmetric matrices by the homotopy method. IMA J. Numer. Anal. 9 (1990) 331-342
    • (1990) IMA J. Numer. Anal. , vol.9 , pp. 331-342
    • Chu, M.T.1
  • 79
    • 0039546401 scopus 로고
    • A continuous Jacobi-like approach to the simultaneous reduction of real matrices
    • Chu M.T. A continuous Jacobi-like approach to the simultaneous reduction of real matrices. Linear Algebra Appl. 147 (1991) 75-96
    • (1991) Linear Algebra Appl. , vol.147 , pp. 75-96
    • Chu, M.T.1
  • 80
    • 0001825184 scopus 로고
    • Homotopy methods for general λ-matrix problems
    • Chu M.T., Li T.-Y., and Sauer T. Homotopy methods for general λ-matrix problems. SIAM J. Matrix Anal. Appl. 9 (1988) 528-536
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 528-536
    • Chu, M.T.1    Li, T.-Y.2    Sauer, T.3
  • 81
    • 0016973951 scopus 로고
    • A switching-parameter algorithm for finding multiple solutions of nonlinear resistive circuits
    • Chua L.O., and Ushida A. A switching-parameter algorithm for finding multiple solutions of nonlinear resistive circuits. Circuit Theory and Appl. 4 (1976) 215-239
    • (1976) Circuit Theory and Appl. , vol.4 , pp. 215-239
    • Chua, L.O.1    Ushida, A.2
  • 82
    • 51249181010 scopus 로고
    • Symmetry breakdown from bifurcation
    • Cicogna G. Symmetry breakdown from bifurcation. Lett. Nuovo Cimento 31 (1981) 600-602
    • (1981) Lett. Nuovo Cimento , vol.31 , pp. 600-602
    • Cicogna, G.1
  • 83
    • 0039472683 scopus 로고
    • The use of symmetry in bifurcation calculations and its application to the Bénard problem
    • Cliffe K.A., and Winters K.H. The use of symmetry in bifurcation calculations and its application to the Bénard problem. J. Comput. Phys. 67 (1986) 310-326
    • (1986) J. Comput. Phys. , vol.67 , pp. 310-326
    • Cliffe, K.A.1    Winters, K.H.2
  • 84
    • 0141937371 scopus 로고
    • Rate of convergence of several conjugate gradient algorithms
    • Cohen A.I. Rate of convergence of several conjugate gradient algorithms. SIAM J. Numer. Anal. 9 (1972) 248-259
    • (1972) SIAM J. Numer. Anal. , vol.9 , pp. 248-259
    • Cohen, A.I.1
  • 85
    • 0012072679 scopus 로고
    • Solution rays for a class of complementarity problems
    • Cottle R.W. Solution rays for a class of complementarity problems. Math. Programming Study 1 (1974) 58-70
    • (1974) Math. Programming Study , vol.1 , pp. 58-70
    • Cottle, R.W.1
  • 86
    • 49949131682 scopus 로고
    • Complementary pivot theory of mathematical programming
    • Cottle R.W., and Dantzig G.B. Complementary pivot theory of mathematical programming. Linear Algebra Appl. 1 (1968) 103-125
    • (1968) Linear Algebra Appl. , vol.1 , pp. 103-125
    • Cottle, R.W.1    Dantzig, G.B.2
  • 87
    • 0018155008 scopus 로고
    • On the solution of large structured linear complementarity problems: The block partitioned case
    • Cottle R.W., Golub G.H., and Sacher R.S. On the solution of large structured linear complementarity problems: The block partitioned case. Appl. Math. Optim. 4 (1978) 347-363
    • (1978) Appl. Math. Optim. , vol.4 , pp. 347-363
    • Cottle, R.W.1    Golub, G.H.2    Sacher, R.S.3
  • 89
    • 0000243546 scopus 로고
    • Discrete groups generated by reflections
    • Coxeter H.S.M. Discrete groups generated by reflections. Ann. of Math. 6 (1934) 13-29
    • (1934) Ann. of Math. , vol.6 , pp. 13-29
    • Coxeter, H.S.M.1
  • 91
  • 92
    • 0342636834 scopus 로고
    • On Numerical Approximation in Bifurcation Theory
    • Masson, New York
    • Crouzeix M., and Rappaz J. On Numerical Approximation in Bifurcation Theory. RMA (1990), Masson, New York
    • (1990) RMA
    • Crouzeix, M.1    Rappaz, J.2
  • 93
    • 0025417986 scopus 로고
    • On the computation of manifolds of fold points for parameter-dependent problems
    • Dai R.-X., and Rheinboldt W.C. On the computation of manifolds of fold points for parameter-dependent problems. SIAM J. Numer. Anal. 27 (1990) 437-446
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 437-446
    • Dai, R.-X.1    Rheinboldt, W.C.2
  • 94
    • 34249832310 scopus 로고
    • A variable dimension algorithm with the Dantzig-Wolfe decomposition for structured stationary point problems
    • Dai Y., Sekitani K., and Yamamoto Y. A variable dimension algorithm with the Dantzig-Wolfe decomposition for structured stationary point problems. Z. Oper. Res. 36 (1992) 23-53
    • (1992) Z. Oper. Res. , vol.36 , pp. 23-53
    • Dai, Y.1    Sekitani, K.2    Yamamoto, Y.3
  • 95
    • 33646991405 scopus 로고
    • The path following algorithm for stationary point problems on polyhedral cones
    • Dai Y., and Yamamoto Y. The path following algorithm for stationary point problems on polyhedral cones. J. Oper. Res. Soc. Japan 32 (1989) 286-309
    • (1989) J. Oper. Res. Soc. Japan , vol.32 , pp. 286-309
    • Dai, Y.1    Yamamoto, Y.2
  • 97
    • 0000615832 scopus 로고
    • On a new method of numerical solution of systems of nonlinear equations
    • in Russian
    • in Russian. Davidenko D. On a new method of numerical solution of systems of nonlinear equations. Dokl. Akad. Nauk USSR 88 (1953) 601-602
    • (1953) Dokl. Akad. Nauk USSR , vol.88 , pp. 601-602
    • Davidenko, D.1
  • 100
    • 0002826423 scopus 로고
    • Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points
    • Dellnitz M., and Werner B. Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points. J. Comput. Appl. Math. 26 (1989) 97-123
    • (1989) J. Comput. Appl. Math. , vol.26 , pp. 97-123
    • Dellnitz, M.1    Werner, B.2
  • 101
    • 0001259993 scopus 로고
    • On steplength algorithms for a class of continuation methods
    • Den Heijer C., and Rheinboldt W.C. On steplength algorithms for a class of continuation methods. SIAM J. Numer. Anal. 18 (1981) 925-948
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 925-948
    • Den Heijer, C.1    Rheinboldt, W.C.2
  • 104
    • 0023401540 scopus 로고
    • Efficient numerical pathfollowing beyond critical points
    • Deuflhard P., Fiedler B., and Kunkel P. Efficient numerical pathfollowing beyond critical points. SIAM J. Numer. Anal. 24 (1987) 912-927
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 912-927
    • Deuflhard, P.1    Fiedler, B.2    Kunkel, P.3
  • 105
    • 0001820687 scopus 로고
    • Affine invariant convergence theorems for Newton's method and extensions to related methods
    • Deuflhard P., and Heindl G. Affine invariant convergence theorems for Newton's method and extensions to related methods. SIAM Numer. Anal. 16 (1979) 1-10
    • (1979) SIAM Numer. Anal. , vol.16 , pp. 1-10
    • Deuflhard, P.1    Heindl, G.2
  • 106
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems. Part I: Bifurcation in finite dimensions
    • Doedel E., Keller H.B., and Kernévez J.P. Numerical analysis and control of bifurcation problems. Part I: Bifurcation in finite dimensions. Internat. J. Bifurcation Chaos 1 (1991) 493-520
    • (1991) Internat. J. Bifurcation Chaos , vol.1 , pp. 493-520
    • Doedel, E.1    Keller, H.B.2    Kernévez, J.P.3
  • 107
    • 0000378934 scopus 로고
    • Numerical analysis and control of bifurcation problems. Part II: Bifurcation in infinite dimensions
    • Doedel E., Keller H.B., and Kernévez J.P. Numerical analysis and control of bifurcation problems. Part II: Bifurcation in infinite dimensions. Internat. J. Bifurcation Chaos 1 (1991) 745-772
    • (1991) Internat. J. Bifurcation Chaos , vol.1 , pp. 745-772
    • Doedel, E.1    Keller, H.B.2    Kernévez, J.P.3
  • 110
    • 34250452611 scopus 로고
    • Homotopies for the computation of fixed points
    • Eaves B.C. Homotopies for the computation of fixed points. Math. Programming 3 (1972) 1-22
    • (1972) Math. Programming , vol.3 , pp. 1-22
    • Eaves, B.C.1
  • 111
    • 0012226424 scopus 로고
    • A short course in solving equations with PL homotopies
    • Cottle R.W., and Lemke C.E. (Eds). Providence, RI
    • Eaves B.C. A short course in solving equations with PL homotopies. In: Cottle R.W., and Lemke C.E. (Eds). Nonlinear Programming, SIAM-AMS Proc. 9. Providence, RI (1976) 73-143
    • (1976) Nonlinear Programming, SIAM-AMS Proc. 9 , pp. 73-143
    • Eaves, B.C.1
  • 112
    • 0037479016 scopus 로고
    • A Course in Triangulations for Solving Equations with Deformations
    • Springer, New York
    • Eaves B.C. A Course in Triangulations for Solving Equations with Deformations. Lecture Notes in Economics and Mathematical Systems 234 (1984), Springer, New York
    • (1984) Lecture Notes in Economics and Mathematical Systems , vol.234
    • Eaves, B.C.1
  • 113
    • 34250456846 scopus 로고
    • Homotopies for computation of fixed points on unbounded regions
    • Eaves B.C., and Saigal R. Homotopies for computation of fixed points on unbounded regions. Math. Programming 3 (1972) 225-237
    • (1972) Math. Programming , vol.3 , pp. 225-237
    • Eaves, B.C.1    Saigal, R.2
  • 114
    • 0016918552 scopus 로고
    • The solution of systems of piecewise linear equations
    • Eaves B.C., and Scarf H. The solution of systems of piecewise linear equations. Math. Oper. Res. 1 (1976) 1-27
    • (1976) Math. Oper. Res. , vol.1 , pp. 1-27
    • Eaves, B.C.1    Scarf, H.2
  • 115
    • 0021477123 scopus 로고
    • Equivalence of surface density and average directional density
    • Eaves B.C., and Yorke J.A. Equivalence of surface density and average directional density. Math. Oper. Res. 9 (1984) 363-375
    • (1984) Math. Oper. Res. , vol.9 , pp. 363-375
    • Eaves, B.C.1    Yorke, J.A.2
  • 117
    • 70350653903 scopus 로고
    • Application of group theory to the method of finite elements
    • ETH
    • Fässler A. Application of group theory to the method of finite elements. PhD thesis (1976), ETH
    • (1976) PhD thesis
    • Fässler, A.1
  • 118
    • 0000405864 scopus 로고
    • CANDYS/QA - A software system for the qualitative analysis of nonlinear dynamical systems
    • to appear
    • to appear. Feudel U., and Jansen W. CANDYS/QA - A software system for the qualitative analysis of nonlinear dynamical systems. Bifurcation & Chaos (1992)
    • (1992) Bifurcation & Chaos
    • Feudel, U.1    Jansen, W.2
  • 120
    • 70350653902 scopus 로고
    • Fiacco A.V. (Ed), North-Holland, New York
    • In: Fiacco A.V. (Ed). Sensitivity, Stability and Parametric Analysis. Mathematical Programming Study 21 (1984), North-Holland, New York
    • (1984) Mathematical Programming Study , vol.21
  • 122
    • 0004599093 scopus 로고
    • On the discretization error of parametrized nonlinear equations
    • Fink J.P., and Rheinboldt W.C. On the discretization error of parametrized nonlinear equations. SIAM J. Numer. Anal. 20 (1983) 732-746
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 732-746
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 123
    • 0004623926 scopus 로고
    • Solution manifolds and submanifolds of parametrized equations and their discretization errors
    • Fink J.P., and Rheinboldt W.C. Solution manifolds and submanifolds of parametrized equations and their discretization errors. Numer. Math. 45 (1984) 323-343
    • (1984) Numer. Math. , vol.45 , pp. 323-343
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 124
    • 0022107802 scopus 로고
    • Local error estimates for parametrized nonlinear equations
    • Fink J.P., and Rheinboldt W.C. Local error estimates for parametrized nonlinear equations. SIAM J. Numer. Anal. 22 (1985) 729-735
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 729-735
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 125
    • 0022767063 scopus 로고
    • Folds on the solution manifold of a parametrized equation
    • Fink J.P., and Rheinboldt W.C. Folds on the solution manifold of a parametrized equation. SIAM J. Numer. Anal. 23 (1986) 693-706
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 693-706
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 126
    • 0023366430 scopus 로고
    • A geometric framework for the numerical study of singular points
    • Fink J.P., and Rheinboldt W.C. A geometric framework for the numerical study of singular points. SIAM J. Numer. Anal. 24 (1987) 618-633
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 618-633
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 128
    • 0001696328 scopus 로고
    • Simplizialzerlegungen von beschränkter Flachheit
    • Freudenthal H. Simplizialzerlegungen von beschränkter Flachheit. Ann. of Math. 43 (1942) 580-582
    • (1942) Ann. of Math. , vol.43 , pp. 580-582
    • Freudenthal, H.1
  • 129
    • 0021518482 scopus 로고
    • Variable dimension complexes. Part I: Basic theory
    • Freund R.M. Variable dimension complexes. Part I: Basic theory. Math. Oper. Res. 9 (1984) 479-497
    • (1984) Math. Oper. Res. , vol.9 , pp. 479-497
    • Freund, R.M.1
  • 130
    • 0021522426 scopus 로고
    • Variable dimension complexes. Part II: A unified approach to some combinatorial lemmas in topology
    • Freund R.M. Variable dimension complexes. Part II: A unified approach to some combinatorial lemmas in topology. Math. Oper. Res. 9 (1984) 498-509
    • (1984) Math. Oper. Res. , vol.9 , pp. 498-509
    • Freund, R.M.1
  • 131
    • 0026369841 scopus 로고
    • A potential-function reduction algorithm for solving a linear program directly from an infeasible "warm start"
    • Ser. B 52. Interior Point Methods for Linear Programming: Theory and Practice. Roos C., and Vial J.-P. (Eds), Mathematical Programming Society, North-Holland, New York
    • Ser. B 52. Freund R.M. A potential-function reduction algorithm for solving a linear program directly from an infeasible "warm start". In: Roos C., and Vial J.-P. (Eds). Interior Point Methods for Linear Programming: Theory and Practice. Math. Programming (1991), Mathematical Programming Society, North-Holland, New York 441-446
    • (1991) Math. Programming , pp. 441-446
    • Freund, R.M.1
  • 134
  • 135
    • 0001710175 scopus 로고
    • Relations between several path following algorithms and local and global Newton methods
    • Garcia C.B., and Gould F.J. Relations between several path following algorithms and local and global Newton methods. SIAM Rev. 22 (1980) 263-274
    • (1980) SIAM Rev. , vol.22 , pp. 263-274
    • Garcia, C.B.1    Gould, F.J.2
  • 136
    • 0000641893 scopus 로고
    • Finding all solutions to polynomial systems and other systems of equations
    • Garcia C.B., and Zangwill W.I. Finding all solutions to polynomial systems and other systems of equations. Math. Programming 16 (1979) 159-176
    • (1979) Math. Programming , vol.16 , pp. 159-176
    • Garcia, C.B.1    Zangwill, W.I.2
  • 138
    • 0041051619 scopus 로고
    • Two methods for the numerical detection of Hopf bifurcations
    • Bifurcation and Chaos: Analysis, Algorithms, Applications. Seydel R., Schneider F.W., Küpper T., and Troger H. (Eds), Birkhäuser, Englewood Cliffs, NJ
    • Garratt T.J., Moore G., and Spence A. Two methods for the numerical detection of Hopf bifurcations. In: Seydel R., Schneider F.W., Küpper T., and Troger H. (Eds). Bifurcation and Chaos: Analysis, Algorithms, Applications. ISNM 97 (1991), Birkhäuser, Englewood Cliffs, NJ 129-134
    • (1991) ISNM , vol.97 , pp. 129-134
    • Garratt, T.J.1    Moore, G.2    Spence, A.3
  • 140
    • 33646992530 scopus 로고
    • A numerically stable update for simplicial algorithms
    • Numerical Solution of Nonlinear Equations. Allgower E.L., Glashoff K., and Peitgen H.-O. (Eds), Springer, Basel
    • Georg K. A numerically stable update for simplicial algorithms. In: Allgower E.L., Glashoff K., and Peitgen H.-O. (Eds). Numerical Solution of Nonlinear Equations. Lecture Notes in Math. 878 (1981), Springer, Basel 117-127
    • (1981) Lecture Notes in Math. , vol.878 , pp. 117-127
    • Georg, K.1
  • 141
    • 0003938147 scopus 로고
    • On tracing an implicitly defined curve by quasi-Newton steps and calculating bifurcation by local perturbation
    • Georg K. On tracing an implicitly defined curve by quasi-Newton steps and calculating bifurcation by local perturbation. SIAM J. Sci. Stat. Comput. 2 (1981) 35-50
    • (1981) SIAM J. Sci. Stat. Comput. , vol.2 , pp. 35-50
    • Georg, K.1
  • 143
    • 0003194891 scopus 로고
    • A note on stepsize control for numerical curve following
    • Eaves B.C., Gould F.J., Peitgen H.-O., and Todd M.J. (Eds), Plenum Press, Germany
    • Georg K. A note on stepsize control for numerical curve following. In: Eaves B.C., Gould F.J., Peitgen H.-O., and Todd M.J. (Eds). Homotopy Methods and Global Convergence (1983), Plenum Press, Germany 145-154
    • (1983) Homotopy Methods and Global Convergence , pp. 145-154
    • Georg, K.1
  • 144
    • 70350683695 scopus 로고
    • An introduction to PL algorithms
    • Computational Solution of Nonlinear Systems of Equations. Allgower E.L., and Georg K. (Eds), American Mathematical Society, New York
    • Georg K. An introduction to PL algorithms. In: Allgower E.L., and Georg K. (Eds). Computational Solution of Nonlinear Systems of Equations. Lectures in Applied Mathematics 26 (1990), American Mathematical Society, New York 207-236
    • (1990) Lectures in Applied Mathematics , vol.26 , pp. 207-236
    • Georg, K.1
  • 145
    • 0040725599 scopus 로고
    • Approximation of integrals for boundary element methods
    • Georg K. Approximation of integrals for boundary element methods. SIAM J. Sci. Stat. Comput. 12 (1991) 443-453
    • (1991) SIAM J. Sci. Stat. Comput. , vol.12 , pp. 443-453
    • Georg, K.1
  • 146
    • 0041309107 scopus 로고
    • Exploiting symmetry in solving linear equations
    • Bifurcation and Symmetry. Allgower E.L., Böhmer K., and Golubitsky M. (Eds), Birkhäuser, Providence, RI
    • Georg K., and Miranda R. Exploiting symmetry in solving linear equations. In: Allgower E.L., Böhmer K., and Golubitsky M. (Eds). Bifurcation and Symmetry. ISNM 104 (1992), Birkhäuser, Providence, RI 157-168
    • (1992) ISNM 104 , pp. 157-168
    • Georg, K.1    Miranda, R.2
  • 147
    • 0041309106 scopus 로고
    • Symmetry aspects in numerical linear algebra with applications to boundary element methods
    • Exploiting Symmetry in Applied and Numerical Analysis. Allgower E.L., Georg K., and Miranda R. (Eds), American Mathematical Society, Basel
    • Georg K., and Miranda R. Symmetry aspects in numerical linear algebra with applications to boundary element methods. In: Allgower E.L., Georg K., and Miranda R. (Eds). Exploiting Symmetry in Applied and Numerical Analysis. Lectures in Applied Mathematics 29 (1993), American Mathematical Society, Basel 213-228
    • (1993) Lectures in Applied Mathematics , vol.29 , pp. 213-228
    • Georg, K.1    Miranda, R.2
  • 148
    • 84968466678 scopus 로고
    • Some error estimates for the numerical approximation of surface integrals
    • Georg K., and Tausch J. Some error estimates for the numerical approximation of surface integrals. Math. Comp. 62 (1993) 755-763
    • (1993) Math. Comp. , vol.62 , pp. 755-763
    • Georg, K.1    Tausch, J.2
  • 150
    • 0020592918 scopus 로고
    • A globally convergent algorithm based on imbedding and parametric optimization
    • Gfrerer H., Guddat J., and Wacker H.-J. A globally convergent algorithm based on imbedding and parametric optimization. Computing 30 (1983) 225-252
    • (1983) Computing , vol.30 , pp. 225-252
    • Gfrerer, H.1    Guddat, J.2    Wacker, H.-J.3
  • 151
    • 0347518372 scopus 로고
    • Path-following for Kuhn-Tucker curves by an active set strategy
    • System and Optimization. Baghi A., and Jongen H.T. (Eds), Springer
    • Gfrerer H., Guddat J., Wacker H.-J., and Zulehner W. Path-following for Kuhn-Tucker curves by an active set strategy. In: Baghi A., and Jongen H.T. (Eds). System and Optimization. Lect. Notes Contr. Inf. Sc. 66 (1985), Springer 111-132
    • (1985) Lect. Notes Contr. Inf. Sc. , vol.66 , pp. 111-132
    • Gfrerer, H.1    Guddat, J.2    Wacker, H.-J.3    Zulehner, W.4
  • 153
    • 0022808235 scopus 로고
    • On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method
    • Gill P.E., Murray W., Saunders M.A., Tomlin J.A., and Wright M.H. On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method. Math. Programming 36 (1986) 183-209
    • (1986) Math. Programming , vol.36 , pp. 183-209
    • Gill, P.E.1    Murray, W.2    Saunders, M.A.3    Tomlin, J.A.4    Wright, M.H.5
  • 154
    • 0000360737 scopus 로고
    • Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems
    • Glowinski R., Keller H.B., and Reinhart L. Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems. SIAM J. Sci. Statist. Comput. 6 (1985) 793-832
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 793-832
    • Glowinski, R.1    Keller, H.B.2    Reinhart, L.3
  • 155
    • 33646991266 scopus 로고
    • Stückweise lineare Approximation implizit definierter Mannigfaltigkeiten
    • University of Hamburg, Berlin
    • Gnutzmann S. Stückweise lineare Approximation implizit definierter Mannigfaltigkeiten. PhD thesis (1989), University of Hamburg, Berlin
    • (1989) PhD thesis
    • Gnutzmann, S.1
  • 161
    • 0026876871 scopus 로고
    • Path-following methods for linear programming
    • Gonzaga C.C. Path-following methods for linear programming. SIAM Rev. 34 (1992) 167-224
    • (1992) SIAM Rev. , vol.34 , pp. 167-224
    • Gonzaga, C.C.1
  • 162
    • 0038020779 scopus 로고
    • Homological methods in fixed point theory of multivalued maps
    • Górniewicz L. Homological methods in fixed point theory of multivalued maps. Diss. Math. 129 (1976)
    • (1976) Diss. Math. , vol.129
    • Górniewicz, L.1
  • 163
    • 12444295135 scopus 로고
    • Complementary Pivoting on a Pseudomanifold Structure with Applications on the Decision Sciences
    • Heldermann, New York
    • Gould F.J., and Tolle J.W. Complementary Pivoting on a Pseudomanifold Structure with Applications on the Decision Sciences. Sigma Series in Applied Mathematics 2 (1983), Heldermann, New York
    • (1983) Sigma Series in Applied Mathematics , vol.2
    • Gould, F.J.1    Tolle, J.W.2
  • 164
    • 0022384709 scopus 로고
    • On solving nonlinear equations with simple singularities or nearly singular solutions
    • Griewank A. On solving nonlinear equations with simple singularities or nearly singular solutions. SIAM Rev. 27 (1985) 537-563
    • (1985) SIAM Rev. , vol.27 , pp. 537-563
    • Griewank, A.1
  • 167
    • 0021382437 scopus 로고
    • Characterization and computation of generalized turning points
    • Griewank A., and Reddien G.W. Characterization and computation of generalized turning points. SIAM J. Numer. Anal. 21 (1984) 176-185
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 176-185
    • Griewank, A.1    Reddien, G.W.2
  • 168
    • 70350668754 scopus 로고
    • Computational environments for exploring dynamical systems
    • Guckenheimer J., and Kim S. Computational environments for exploring dynamical systems. Bifurcation & Chaos 1 (1991) 269-276
    • (1991) Bifurcation & Chaos , vol.1 , pp. 269-276
    • Guckenheimer, J.1    Kim, S.2
  • 170
    • 33646992013 scopus 로고
    • Guddat J., Jongen H.T., Kummer B., and Nožička F. (Eds), Akademie, Chichester, England
    • In: Guddat J., Jongen H.T., Kummer B., and Nožička F. (Eds). Parametric Optimization and Related Topics (1987), Akademie, Chichester, England
    • (1987) Parametric Optimization and Related Topics
  • 171
    • 0041809765 scopus 로고
    • Use of group theory in various integral equations
    • Guy J., and Mangeot B. Use of group theory in various integral equations. SIAM J. Appl. Math. 40 (1981) 390-399
    • (1981) SIAM J. Appl. Math. , vol.40 , pp. 390-399
    • Guy, J.1    Mangeot, B.2
  • 173
    • 85067973190 scopus 로고
    • Iterative Solution of Large Sparse Systems of Equations
    • Springer, Stuttgart
    • Hackbusch W. Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences 95 (1994), Springer, Stuttgart
    • (1994) Applied Mathematical Sciences , vol.95
    • Hackbusch, W.1
  • 174
    • 0010085880 scopus 로고
    • The solution of nonlinear equations and of differential equations with two-point boundary conditions
    • Haselgrove C.B. The solution of nonlinear equations and of differential equations with two-point boundary conditions. Comput. J. 4 (1961) 255-259
    • (1961) Comput. J. , vol.4 , pp. 255-259
    • Haselgrove, C.B.1
  • 175
    • 0041178505 scopus 로고
    • Global bifurcation and continuation in the presence of symmetry with an application to solid mechanics
    • Healey T.J. Global bifurcation and continuation in the presence of symmetry with an application to solid mechanics. SIAM J. Math. Anal. 19 (1988) 824-840
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 824-840
    • Healey, T.J.1
  • 176
    • 0023997872 scopus 로고
    • A group theoretic approach to computational bifurcation problems with symmetry
    • Healey T.J. A group theoretic approach to computational bifurcation problems with symmetry. Comput. Meth. Appl. Mech. Engrg. 67 (1988) 257-295
    • (1988) Comput. Meth. Appl. Mech. Engrg. , vol.67 , pp. 257-295
    • Healey, T.J.1
  • 177
    • 0004299147 scopus 로고
    • Symmetry and equivariance in nonlinear elastostatics, Part I
    • Healey T.J. Symmetry and equivariance in nonlinear elastostatics, Part I. Arch. Rational Mech. Anal. 105 (1989) 205-228
    • (1989) Arch. Rational Mech. Anal. , vol.105 , pp. 205-228
    • Healey, T.J.1
  • 178
    • 0026111067 scopus 로고
    • Exact block diagonalization of large eigenvalue problems for structures with symmetry
    • Healey T.J., and Treacy J.A. Exact block diagonalization of large eigenvalue problems for structures with symmetry. Internat. J. Numer. Methods Engrg. 31 (1991) 265-285
    • (1991) Internat. J. Numer. Methods Engrg. , vol.31 , pp. 265-285
    • Healey, T.J.1    Treacy, J.A.2
  • 179
    • 0040145941 scopus 로고
    • Complex bifurcation
    • CALTECH, Berlin
    • Henderson M.E. Complex bifurcation. PhD thesis (1985), CALTECH, Berlin
    • (1985) PhD thesis
    • Henderson, M.E.1
  • 180
  • 181
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Hestenes M.R., and Stiefel E. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards 49 (1952) 409-436
    • (1952) J. Res. Nat. Bur. Standards , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 183
    • 84966202377 scopus 로고
    • A proof of the nonretractibility of a cell onto its boundary
    • Hirsch M.W. A proof of the nonretractibility of a cell onto its boundary. Proc. Amer. Math. Soc. 14 (1963) 364-365
    • (1963) Proc. Amer. Math. Soc. , vol.14 , pp. 364-365
    • Hirsch, M.W.1
  • 186
    • 0012853542 scopus 로고
    • DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
    • Holodniok M., and Kubíček M. DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations. J. Comput. Phys. 55 (1984) 254-267
    • (1984) J. Comput. Phys. , vol.55 , pp. 254-267
    • Holodniok, M.1    Kubíček, M.2
  • 187
    • 0027641927 scopus 로고
    • Computational methods for bifurcation problems with symmetries on the manifold
    • Hong B. Computational methods for bifurcation problems with symmetries on the manifold. SIAM J. Numer. Anal. 30 (1993) 1134-1154
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1134-1154
    • Hong, B.1
  • 190
    • 0039177055 scopus 로고
    • Nonlinear eigenvalue problems - Prediction of bifurcation points and branch switching
    • Univ. of Göteborg
    • Huitfeldt J. Nonlinear eigenvalue problems - Prediction of bifurcation points and branch switching. Technical Report 17 (1991), Univ. of Göteborg
    • (1991) Technical Report 17
    • Huitfeldt, J.1
  • 191
    • 0001099552 scopus 로고
    • A new algorithm for numerical path following applied to an example from hydrodynamical flow
    • Huitfeldt J., and Ruhe A. A new algorithm for numerical path following applied to an example from hydrodynamical flow. SIAM J. Sci. Statist. Comput. 11 (1990) 1181-1192
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 1181-1192
    • Huitfeldt, J.1    Ruhe, A.2
  • 192
    • 14244264121 scopus 로고
    • Methods of fast automatic differentiation and applications
    • Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokyo, Sweden
    • Iri M., and Kubota K. Methods of fast automatic differentiation and applications. Research Memorandum RMI 87-02 (1987), Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokyo, Sweden
    • (1987) Research Memorandum RMI 87-02
    • Iri, M.1    Kubota, K.2
  • 193
    • 33645967051 scopus 로고
    • Topological bifurcation
    • Matzeu M., and Vignoli A. (Eds), Birkhäuser
    • Ize J. Topological bifurcation. In: Matzeu M., and Vignoli A. (Eds). Nonlinear Analysis (1993), Birkhäuser
    • (1993) Nonlinear Analysis
    • Ize, J.1
  • 194
    • 0002448538 scopus 로고
    • Periodic solutions of x″ + f(x, t) = 0 via the Poincaré-Birkhoff theorem
    • Jacobowitz H. Periodic solutions of x″ + f(x, t) = 0 via the Poincaré-Birkhoff theorem. J. Differential Equations 20 (1976) 37-52
    • (1976) J. Differential Equations , vol.20 , pp. 37-52
    • Jacobowitz, H.1
  • 195
    • 0040843221 scopus 로고
    • A note on computing simple bifurcation points
    • Janovský V. A note on computing simple bifurcation points. Computing 43 (1989) 27-36
    • (1989) Computing , vol.43 , pp. 27-36
    • Janovský, V.1
  • 196
    • 0012943062 scopus 로고
    • Numerical treatment of bifurcation branches by adaptive condensation
    • Numerical Methods for Bifurcation Problems. Küpper T., Mittelmann H.D., and Weber H. (Eds), Birkhäuser, Boston, MA
    • Jarausch H., and Mackens W. Numerical treatment of bifurcation branches by adaptive condensation. In: Küpper T., Mittelmann H.D., and Weber H. (Eds). Numerical Methods for Bifurcation Problems. ISNM 70 (1984), Birkhäuser, Boston, MA
    • (1984) ISNM , vol.70
    • Jarausch, H.1    Mackens, W.2
  • 197
    • 0001548361 scopus 로고
    • Solving large nonlinear systems of equations by an adaptive condensation process
    • Jarausch H., and Mackens W. Solving large nonlinear systems of equations by an adaptive condensation process. Numer. Math. 50 (1987) 633-653
    • (1987) Numer. Math. , vol.50 , pp. 633-653
    • Jarausch, H.1    Mackens, W.2
  • 198
    • 0000808907 scopus 로고
    • Convergence cones near bifurcation
    • Jepson A.D., and Decker D.W. Convergence cones near bifurcation. SIAM J. Numer. Anal. 23 (1986) 959-975
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 959-975
    • Jepson, A.D.1    Decker, D.W.2
  • 200
    • 0000164939 scopus 로고
    • One codimensional Wecken type theorems
    • Jezierski J. One codimensional Wecken type theorems. Forum Math. (1993) 421-439
    • (1993) Forum Math. , pp. 421-439
    • Jezierski, J.1
  • 203
    • 0012493186 scopus 로고
    • On parametric nonlinear programming
    • Jongen H.T., and Weber G.-W. On parametric nonlinear programming. Ann. Oper. Res. 27 (1990) 253-284
    • (1990) Ann. Oper. Res. , vol.27 , pp. 253-284
    • Jongen, H.T.1    Weber, G.-W.2
  • 204
    • 0000025652 scopus 로고
    • On the local structure of the feasible set in semi-infinite optimization
    • Birkhäuser, New York
    • Jongen H.T., and Zwier G. On the local structure of the feasible set in semi-infinite optimization. ISNM 72 (1985), Birkhäuser, New York 185-202
    • (1985) ISNM , vol.72 , pp. 185-202
    • Jongen, H.T.1    Zwier, G.2
  • 205
    • 0004219579 scopus 로고
    • Newton's method for generalized equations
    • available from National Technical Information Service under accession number AD A077 096, University of Wisconsin, Basel
    • available from National Technical Information Service under accession number AD A077 096. Josephy N.H. Newton's method for generalized equations. Technical Report 1965 (1979), University of Wisconsin, Basel
    • (1979) Technical Report 1965
    • Josephy, N.H.1
  • 207
    • 70350697759 scopus 로고
    • Variable dimension simplicial algorithm for balanced games
    • Tilburg Univ., England
    • Kamiya K., and Talman A.J.J. Variable dimension simplicial algorithm for balanced games. Technical Report 9025 (1990), Tilburg Univ., England
    • (1990) Technical Report 9025
    • Kamiya, K.1    Talman, A.J.J.2
  • 208
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • Karmarkar N.K. A new polynomial-time algorithm for linear programming. Combinatorica 4 (1984) 373-395
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.K.1
  • 209
    • 34249921043 scopus 로고
    • Computational results of an interior point algorithm for large scale linear programming
    • Ser. B. Interior Point Methods for Linear Programming: Theory and Practice. Roos C., and Vial J.-P. (Eds), Mathematical Programming Society, North-Holland, The Netherlands
    • Ser. B. Karmarkar N.K., and Ramakrishnan K.G. Computational results of an interior point algorithm for large scale linear programming. In: Roos C., and Vial J.-P. (Eds). Interior Point Methods for Linear Programming: Theory and Practice. Math. Programming 52 (1991), Mathematical Programming Society, North-Holland, The Netherlands 555-586
    • (1991) Math. Programming , vol.52 , pp. 555-586
    • Karmarkar, N.K.1    Ramakrishnan, K.G.2
  • 210
    • 69849105337 scopus 로고
    • An algorithm for solving nonlinear resistive networks
    • Katzenelson J. An algorithm for solving nonlinear resistive networks. Bell System Tech. J. 44 (1965) 1605-1620
    • (1965) Bell System Tech. J. , vol.44 , pp. 1605-1620
    • Katzenelson, J.1
  • 211
    • 33646992573 scopus 로고
    • An interval step control for continuation methods
    • to appear
    • to appear. Kearfott R.B. An interval step control for continuation methods. Math. Comp. (1989)
    • (1989) Math. Comp.
    • Kearfott, R.B.1
  • 212
    • 0000916423 scopus 로고
    • Interval arithmetic techniques in the computational solution of nonlinear systems of equations: Introduction, examples and comparisons
    • Computational Solution of Nonlinear Systems of Equations. Allgower E.L., and Georg K. (Eds), American Mathematical Society, Amsterdam
    • Kearfott R.B. Interval arithmetic techniques in the computational solution of nonlinear systems of equations: Introduction, examples and comparisons. In: Allgower E.L., and Georg K. (Eds). Computational Solution of Nonlinear Systems of Equations. Lectures in Applied Mathematics 26 (1990), American Mathematical Society, Amsterdam 337-357
    • (1990) Lectures in Applied Mathematics , vol.26 , pp. 337-357
    • Kearfott, R.B.1
  • 215
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and nonlinear eigenvalue problems
    • Rabinowitz P.H. (Ed), Academic Press, Providence, RI
    • Keller H.B. Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Rabinowitz P.H. (Ed). Applications of Bifurcation Theory (1977), Academic Press, Providence, RI 359-384
    • (1977) Applications of Bifurcation Theory , pp. 359-384
    • Keller, H.B.1
  • 216
    • 0003080367 scopus 로고
    • Global homotopies and Newton methods
    • de Boor C., and Golub G.H. (Eds), Academic Press, New York
    • Keller H.B. Global homotopies and Newton methods. In: de Boor C., and Golub G.H. (Eds). Recent Advances in Numerical Analysis (1978), Academic Press, New York 73-94
    • (1978) Recent Advances in Numerical Analysis , pp. 73-94
    • Keller, H.B.1
  • 217
    • 0142006726 scopus 로고
    • Practical procedures in path following near limit points
    • Glowinski R., and Lions J.-L. (Eds), North-Holland, New York
    • Keller H.B. Practical procedures in path following near limit points. In: Glowinski R., and Lions J.-L. (Eds). Computing Methods in Applied Sciences and Engineering (1982), North-Holland, New York
    • (1982) Computing Methods in Applied Sciences and Engineering
    • Keller, H.B.1
  • 218
    • 0001151327 scopus 로고
    • The bordering algorithm and path following near singular points of higher nullity
    • Keller H.B. The bordering algorithm and path following near singular points of higher nullity. SIAM J. Sci. Statist. Comput 4 (1983) 573-582
    • (1983) SIAM J. Sci. Statist. Comput , vol.4 , pp. 573-582
    • Keller, H.B.1
  • 220
    • 0016993685 scopus 로고
    • A constructive proof of the Brouwer fixed point theorem and computational results
    • Kellogg R.B., Li T.-Y., and Yorke J.A. A constructive proof of the Brouwer fixed point theorem and computational results. SIAM J. Numer. Anal. 13 (1976) 473-483
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 473-483
    • Kellogg, R.B.1    Li, T.-Y.2    Yorke, J.A.3
  • 221
    • 0000564361 scopus 로고
    • A polynomial algorithm in linear programming
    • Khachiyan L.G. A polynomial algorithm in linear programming. Soviet Math. Dokl. 20 (1979) 191-194
    • (1979) Soviet Math. Dokl. , vol.20 , pp. 191-194
    • Khachiyan, L.G.1
  • 223
    • 4544313738 scopus 로고
    • Continuation techniques and interactive software for bifurcation analysis of odes and iterated maps
    • Khibnik A.I., Kuznetsov Y.A., Levitin V.V., and Nikolaev E.V. Continuation techniques and interactive software for bifurcation analysis of odes and iterated maps. Phys. D (1993) 360-371
    • (1993) Phys. D , pp. 360-371
    • Khibnik, A.I.1    Kuznetsov, Y.A.2    Levitin, V.V.3    Nikolaev, E.V.4
  • 224
    • 0002519671 scopus 로고
    • Neue Beiträge zur Riemannschen Funktionentheorie
    • Klein F. Neue Beiträge zur Riemannschen Funktionentheorie. Math. Ann. 21 (1882-1883)
    • (1882) Math. Ann. , vol.21
    • Klein, F.1
  • 225
    • 0042505930 scopus 로고
    • Computational methods for solving the nonlinear complementarity problem
    • Kojima M. Computational methods for solving the nonlinear complementarity problem. Keio Engrg. Rep. 27 (1974) 1-41
    • (1974) Keio Engrg. Rep. , vol.27 , pp. 1-41
    • Kojima, M.1
  • 226
    • 0008522358 scopus 로고
    • 1 mappings in fixed points and complementarity theory
    • 1 mappings in fixed points and complementarity theory. Math. Oper. Res. 3 (1978) 17-36
    • (1978) Math. Oper. Res. , vol.3 , pp. 17-36
    • Kojima, M.1
  • 227
    • 0011282597 scopus 로고
    • A complementarity pivoting approach to parametric programming
    • Kojima M. A complementarity pivoting approach to parametric programming. Math. Oper. Res. 4 (1979) 464-477
    • (1979) Math. Oper. Res. , vol.4 , pp. 464-477
    • Kojima, M.1
  • 228
    • 0021450976 scopus 로고
    • Sensitivity, stability and parametric analysis
    • North-Holland, Setauket, NY
    • Kojima M., and Hirabayashi R. Sensitivity, stability and parametric analysis. Mathematical Programming Study 21 (1984), North-Holland, Setauket, NY 150-198
    • (1984) Mathematical Programming Study , vol.21 , pp. 150-198
    • Kojima, M.1    Hirabayashi, R.2
  • 229
    • 84936450701 scopus 로고
    • A general framework of continuation methods for complementarity problems
    • IBM Almaden Research Center, Amsterdam
    • Kojima M., Megiddo N., and Mizuno S. A general framework of continuation methods for complementarity problems. Technical report (1990), IBM Almaden Research Center, Amsterdam
    • (1990) Technical report
    • Kojima, M.1    Megiddo, N.2    Mizuno, S.3
  • 231
    • 0001217295 scopus 로고
    • Homotopy continuation methods for nonlinear complementarity problems
    • Kojima M., Megiddo N., and Noma T. Homotopy continuation methods for nonlinear complementarity problems. Math. Oper. Res. 16 (1991) 754-774
    • (1991) Math. Oper. Res. , vol.16 , pp. 754-774
    • Kojima, M.1    Megiddo, N.2    Noma, T.3
  • 232
    • 0003212154 scopus 로고
    • A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems
    • Springer
    • Kojima M., Megiddo N., Noma T., and Yoshise A. A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems. Lecture Notes in Computer Science 538 (1991), Springer
    • (1991) Lecture Notes in Computer Science , vol.538
    • Kojima, M.1    Megiddo, N.2    Noma, T.3    Yoshise, A.4
  • 233
    • 0026839261 scopus 로고
    • An interior point potential reduction algorithm for the linear complementarity problem
    • Kojima M., Megiddo N., and Ye Y. An interior point potential reduction algorithm for the linear complementarity problem. Math. Programming 54 (1992) 267-279
    • (1992) Math. Programming , vol.54 , pp. 267-279
    • Kojima, M.1    Megiddo, N.2    Ye, Y.3
  • 234
    • 0001214560 scopus 로고
    • Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems
    • Kojima M., Mizuno S., and Noma T. Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems. Math. Oper. Res. 15 (1990) 662-675
    • (1990) Math. Oper. Res. , vol.15 , pp. 662-675
    • Kojima, M.1    Mizuno, S.2    Noma, T.3
  • 236
    • 0024665751 scopus 로고
    • A polynomial-time algorithm for a class of linear complementarity problems
    • Kojima M., Mizuno S., and Yoshise A. A polynomial-time algorithm for a class of linear complementarity problems. Math. Programming 44 (1989) 1-26
    • (1989) Math. Programming , vol.44 , pp. 1-26
    • Kojima, M.1    Mizuno, S.2    Yoshise, A.3
  • 237
    • 0026171528 scopus 로고
    • An O(√nL) iteration potential reduction algorithm for linear complementarity problems
    • Kojima M., Mizuno S., and Yoshise A. An O(√nL) iteration potential reduction algorithm for linear complementarity problems. Math. Programming 50 (1991) 331-342
    • (1991) Math. Programming , vol.50 , pp. 331-342
    • Kojima, M.1    Mizuno, S.2    Yoshise, A.3
  • 238
    • 33646993072 scopus 로고
    • An extension of Lemke's method to the piecewise linear complementarity problem
    • Kojima M., Nishino H., and Sekine T. An extension of Lemke's method to the piecewise linear complementarity problem. SIAM J. Appl. Math. 31 (1976) 600-613
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 600-613
    • Kojima, M.1    Nishino, H.2    Sekine, T.3
  • 239
    • 0020194141 scopus 로고
    • Variable dimension algorithms: Basic theory, interpretation, and extensions of some existing methods
    • Kojima M., and Yamamoto Y. Variable dimension algorithms: Basic theory, interpretation, and extensions of some existing methods. Math. Programming 24 (1982) 177-215
    • (1982) Math. Programming , vol.24 , pp. 177-215
    • Kojima, M.1    Yamamoto, Y.2
  • 240
    • 0021408608 scopus 로고
    • A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm
    • Kojima M., and Yamamoto Y. A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm. Math. Programming 28 (1984) 288-328
    • (1984) Math. Programming , vol.28 , pp. 288-328
    • Kojima, M.1    Yamamoto, Y.2
  • 241
    • 0023586285 scopus 로고
    • Heterogeneous azeotropic distillation - Homotopy-continuation methods
    • Kovach J.W., and Seider W.D. Heterogeneous azeotropic distillation - Homotopy-continuation methods. Comput. Chem. Engrg. 11 (1987) 593-605
    • (1987) Comput. Chem. Engrg. , vol.11 , pp. 593-605
    • Kovach, J.W.1    Seider, W.D.2
  • 243
    • 0016931444 scopus 로고
    • Algorithm 502. Dependence of solutions of nonlinear systems on a parameter
    • Kubíček M. Algorithm 502. Dependence of solutions of nonlinear systems on a parameter. ACM Trans. Math. Software 2 (1976) 98-107
    • (1976) ACM Trans. Math. Software , vol.2 , pp. 98-107
    • Kubíček, M.1
  • 244
    • 0001011343 scopus 로고
    • Simplicial approximation of fixed points
    • Kuhn H.W. Simplicial approximation of fixed points. Proc. Nat. Acad. Sci. USA 61 (1968) 1238-1242
    • (1968) Proc. Nat. Acad. Sci. USA , vol.61 , pp. 1238-1242
    • Kuhn, H.W.1
  • 245
    • 0141972036 scopus 로고
    • Approximate search for fixed points
    • Zadek L.A., Neustat L.W., and Balakrishnan A.V. (Eds), Academic Press, New York
    • Kuhn H.W. Approximate search for fixed points. In: Zadek L.A., Neustat L.W., and Balakrishnan A.V. (Eds). Computing Methods in Optimization Problems 2 (1969), Academic Press, New York 199-211
    • (1969) Computing Methods in Optimization Problems , vol.2 , pp. 199-211
    • Kuhn, H.W.1
  • 247
    • 0001644591 scopus 로고
    • Bimatrix equilibrium points and mathematical programming
    • Lemke C.E. Bimatrix equilibrium points and mathematical programming. Management Sci. 11 (1965) 681-689
    • (1965) Management Sci. , vol.11 , pp. 681-689
    • Lemke, C.E.1
  • 248
    • 0141937330 scopus 로고
    • A survey of complementarity theory
    • Cottle R.W., Gianessi F., and Lions J.L. (Eds), Wiley, New York
    • Lemke C.E. A survey of complementarity theory. In: Cottle R.W., Gianessi F., and Lions J.L. (Eds). Variational Inequalities and Complentarity Problems (1980), Wiley, New York
    • (1980) Variational Inequalities and Complentarity Problems
    • Lemke, C.E.1
  • 249
    • 33646992305 scopus 로고
    • On generalizing Shapley's index theory to labelled pseudo manifolds
    • Lemke C.E., and Grotzinger S.J. On generalizing Shapley's index theory to labelled pseudo manifolds. Math. Programming 10 (1976) 245-262
    • (1976) Math. Programming , vol.10 , pp. 245-262
    • Lemke, C.E.1    Grotzinger, S.J.2
  • 250
    • 0000176346 scopus 로고
    • Equilibrium points of bimatrix games
    • Lemke C.E., and Howson J.T. Equilibrium points of bimatrix games. SIAM J. Appl. Math. 12 (1964) 413-423
    • (1964) SIAM J. Appl. Math. , vol.12 , pp. 413-423
    • Lemke, C.E.1    Howson, J.T.2
  • 251
    • 0040740183 scopus 로고
    • An algorithm for symmetric tridiagonal eigen-problems - Divide and conquer with homotopy continuation
    • Li K., and Li T.-Y. An algorithm for symmetric tridiagonal eigen-problems - Divide and conquer with homotopy continuation. SIAM J. Sci. Statist. Comput. 14 (1993) 735-751
    • (1993) SIAM J. Sci. Statist. Comput. , vol.14 , pp. 735-751
    • Li, K.1    Li, T.-Y.2
  • 252
    • 0001745927 scopus 로고
    • Homotopy algorithm for symmetric eigenvalue problems
    • Li T.-Y., and Rhee N.H. Homotopy algorithm for symmetric eigenvalue problems. Numer. Math. 55 (1989) 265-280
    • (1989) Numer. Math. , vol.55 , pp. 265-280
    • Li, T.-Y.1    Rhee, N.H.2
  • 253
    • 0023331578 scopus 로고
    • Numerical solution of a class of deficient polynomial systems
    • Li T.-Y., Sauer T., and Yorke J.A. Numerical solution of a class of deficient polynomial systems. SIAM J. Numer. Anal. 24 (1987) 435-451
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 435-451
    • Li, T.-Y.1    Sauer, T.2    Yorke, J.A.3
  • 254
    • 0001444287 scopus 로고
    • The cheater's homotopy: An efficient procedure for solving systems of polynomial equations
    • Li T.-Y., Sauer T., and Yorke J.A. The cheater's homotopy: An efficient procedure for solving systems of polynomial equations. SIAM J. Numer. Anal. 26 (1989) 1241-1251
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1241-1251
    • Li, T.-Y.1    Sauer, T.2    Yorke, J.A.3
  • 255
    • 0026908926 scopus 로고
    • Nonlinear homotopies for solving deficient polynomial systems with parameters
    • Li T.-Y., and Wang X. Nonlinear homotopies for solving deficient polynomial systems with parameters. SIAM J. Numer. Anal. 29 (1993) 1104-1118
    • (1993) SIAM J. Numer. Anal. , vol.29 , pp. 1104-1118
    • Li, T.-Y.1    Wang, X.2
  • 256
    • 84968512881 scopus 로고
    • Solving real polynomial systems with real homotopies
    • Li T.-Y., and Wang X. Solving real polynomial systems with real homotopies. Math. Comp. 60 (1993) 669-680
    • (1993) Math. Comp. , vol.60 , pp. 669-680
    • Li, T.-Y.1    Wang, X.2
  • 257
    • 84968468997 scopus 로고
    • Homotopy-determinant algorithm for solving nonsymmetric eigenvalue problems
    • to appear
    • to appear. Li T.-Y., and Zeng Z. Homotopy-determinant algorithm for solving nonsymmetric eigenvalue problems. Math. Comp. (1992)
    • (1992) Math. Comp.
    • Li, T.-Y.1    Zeng, Z.2
  • 258
    • 0026821332 scopus 로고
    • Solving eigenvalue problems of real nonsymmetric matrices with real homotopies
    • Li T.-Y., Zeng Z., and Cong L. Solving eigenvalue problems of real nonsymmetric matrices with real homotopies. SIAM J. Numer. Anal. 29 (1992) 229-248
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 229-248
    • Li, T.-Y.1    Zeng, Z.2    Cong, L.3
  • 259
    • 0038961658 scopus 로고
    • Parallel homotopy algorithm for the symmetric tridiagonal eigenvalue problem
    • Li T.-Y., Zhang H., and Sun X.-H. Parallel homotopy algorithm for the symmetric tridiagonal eigenvalue problem. SIAM J. Sci. Statist. Comput. 12 (1991) 469-487
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 469-487
    • Li, T.-Y.1    Zhang, H.2    Sun, X.-H.3
  • 261
    • 0040243239 scopus 로고
    • A posteriori error estimates for parametrized nonlinear equations
    • Wriggers P., and Wagner W. (Eds), Springer, China
    • Liu J.L., and Rheinboldt W.C. A posteriori error estimates for parametrized nonlinear equations. In: Wriggers P., and Wagner W. (Eds). Nonlinear Computational Mechanics (1991), Springer, China 31-46
    • (1991) Nonlinear Computational Mechanics , pp. 31-46
    • Liu, J.L.1    Rheinboldt, W.C.2
  • 262
    • 0005076683 scopus 로고
    • Variable order Adams-Bashforth predictors with an error-stepsize control for continuation methods
    • Lundberg B.N., and Poore A.B. Variable order Adams-Bashforth predictors with an error-stepsize control for continuation methods. SIAM J. Sci. Statist. Comput. 12 (1991) 695-723
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 695-723
    • Lundberg, B.N.1    Poore, A.B.2
  • 263
    • 0042013996 scopus 로고
    • Numerical continuation and singularity detection methods for parametric nonlinear programming
    • Lundberg B.N., and Poore A.B. Numerical continuation and singularity detection methods for parametric nonlinear programming. SIAM J. Optim. 3 (1993) 134-154
    • (1993) SIAM J. Optim. , vol.3 , pp. 134-154
    • Lundberg, B.N.1    Poore, A.B.2
  • 264
    • 70350700845 scopus 로고
    • The interaction of algorithms and architectures for interior point methods
    • Rutgers Univ., Heidelberg
    • Lustig I.J., Marsten R.E., and Shanno D.F. The interaction of algorithms and architectures for interior point methods. Technical Report RRR 36-91 (1991), Rutgers Univ., Heidelberg
    • (1991) Technical Report RRR 36-91
    • Lustig, I.J.1    Marsten, R.E.2    Shanno, D.F.3
  • 265
    • 0011461706 scopus 로고
    • Quadrature over a simplex: Part 2. A representation for the error functional
    • Lyness J.N. Quadrature over a simplex: Part 2. A representation for the error functional. SIAM J. Numer. Anal. 15 (1978) 870-887
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 870-887
    • Lyness, J.N.1
  • 266
    • 70350690644 scopus 로고
    • Quadrature over curved surfaces by extrapolation
    • to appear
    • to appear. Lyness J.N. Quadrature over curved surfaces by extrapolation. Math. Comp. (1993)
    • (1993) Math. Comp.
    • Lyness, J.N.1
  • 267
    • 0024775585 scopus 로고
    • Numerical differentiation of implicitly defined space curves
    • Mackens W. Numerical differentiation of implicitly defined space curves. Computing 41 (1989) 237-260
    • (1989) Computing , vol.41 , pp. 237-260
    • Mackens, W.1
  • 268
    • 0001659901 scopus 로고
    • Interior point methods for linear programming: Just call Newton, Lagrange and Fiacco and Mccormick!
    • Marsten R., Subramanian R., Saltzman M., Lustig I.J., and Shanno D.F. Interior point methods for linear programming: Just call Newton, Lagrange and Fiacco and Mccormick!. Interfaces 20 (1990) 105-116
    • (1990) Interfaces , vol.20 , pp. 105-116
    • Marsten, R.1    Subramanian, R.2    Saltzman, M.3    Lustig, I.J.4    Shanno, D.F.5
  • 269
    • 0016057394 scopus 로고
    • Alternate proofs of the convergence properties of the conjugate-gradient method
    • McCormick G.P., and Ritter K. Alternate proofs of the convergence properties of the conjugate-gradient method. J. Optim. Theory Appl. 13 (1974) 497-518
    • (1974) J. Optim. Theory Appl. , vol.13 , pp. 497-518
    • McCormick, G.P.1    Ritter, K.2
  • 270
    • 70350694369 scopus 로고
    • Preconditioned iterative methods for sparse linear algebra problems arising in circuit simulation
    • to appear
    • to appear. McQuain W.D., Ribbens C.J., Watson L.T., and Melville R.C. Preconditioned iterative methods for sparse linear algebra problems arising in circuit simulation. Comput. Math. Appl. (1993)
    • (1993) Comput. Math. Appl.
    • McQuain, W.D.1    Ribbens, C.J.2    Watson, L.T.3    Melville, R.C.4
  • 271
    • 0002431411 scopus 로고
    • An implementation of a primal-dual interior point method for linear programming
    • McShane K.A., Monma C.L., and Shanno D.F. An implementation of a primal-dual interior point method for linear programming. ORSA J. Comput. 1 (1989) 70-83
    • (1989) ORSA J. Comput. , vol.1 , pp. 70-83
    • McShane, K.A.1    Monma, C.L.2    Shanno, D.F.3
  • 273
    • 0024606578 scopus 로고
    • Boundary behavior of interior point algorithms in linear programming
    • Megiddo N., and Shub M. Boundary behavior of interior point algorithms in linear programming. Math. Oper. Res. 14 (1989) 97-146
    • (1989) Math. Oper. Res. , vol.14 , pp. 97-146
    • Megiddo, N.1    Shub, M.2
  • 274
    • 0002340728 scopus 로고
    • CONKUB: A conversational path-follower for systems of nonlinear equations
    • Mejia R. CONKUB: A conversational path-follower for systems of nonlinear equations. J. Comput. Phys. 63 (1986) 67-84
    • (1986) J. Comput. Phys. , vol.63 , pp. 67-84
    • Mejia, R.1
  • 275
    • 84971971606 scopus 로고
    • Interactive program for continuation of solutions of large systems of nonlinear equations
    • Computational Solution of Nonlinear Systems of Equations. Allgower E.L., and Georg K. (Eds), American Mathematical Society, New York
    • Mejia R. Interactive program for continuation of solutions of large systems of nonlinear equations. In: Allgower E.L., and Georg K. (Eds). Computational Solution of Nonlinear Systems of Equations. Lectures in Applied Mathematics 26 (1990), American Mathematical Society, New York 429-449
    • (1990) Lectures in Applied Mathematics , vol.26 , pp. 429-449
    • Mejia, R.1
  • 276
    • 0020288760 scopus 로고
    • A comparison of methods for determining turning points of nonlinear equations
    • Melhem R.G., and Rheinboldt W.C. A comparison of methods for determining turning points of nonlinear equations. Computing 29 (1982) 201-226
    • (1982) Computing , vol.29 , pp. 201-226
    • Melhem, R.G.1    Rheinboldt, W.C.2
  • 277
    • 0027589008 scopus 로고
    • Sframe: An efficient system for detailed DC simulation of bipolar analog integrated circuits using continuation methods
    • Melville R., Moinian S., Feldmann P., and Watson L.T. Sframe: An efficient system for detailed DC simulation of bipolar analog integrated circuits using continuation methods. Analog Integr. Circuits Signal Process. 3 (1993) 163-180
    • (1993) Analog Integr. Circuits Signal Process. , vol.3 , pp. 163-180
    • Melville, R.1    Moinian, S.2    Feldmann, P.3    Watson, L.T.4
  • 279
    • 0041010223 scopus 로고
    • Zur Lösung parameterabhängiger nichtlinearer Gleichungen mit singulären Jacobi-Matrizen
    • Menzel R., and Schwetlick H. Zur Lösung parameterabhängiger nichtlinearer Gleichungen mit singulären Jacobi-Matrizen. Numer. Math. 30 (1978) 65-79
    • (1978) Numer. Math. , vol.30 , pp. 65-79
    • Menzel, R.1    Schwetlick, H.2
  • 280
    • 0037797920 scopus 로고
    • Parametrization via secant length and application to path following
    • Menzel R., and Schwetlick H. Parametrization via secant length and application to path following. Numer. Math. 47 (1985) 401-412
    • (1985) Numer. Math. , vol.47 , pp. 401-412
    • Menzel, R.1    Schwetlick, H.2
  • 281
    • 0004027434 scopus 로고
    • Applications and extensions of an algorithm that computes fixed points of a certain upper semi-continuous point to set mapping
    • Univ. of Michigan, Providence, RI
    • Merrill O. Applications and extensions of an algorithm that computes fixed points of a certain upper semi-continuous point to set mapping. PhD thesis (1972), Univ. of Michigan, Providence, RI
    • (1972) PhD thesis
    • Merrill, O.1
  • 284
    • 70350696150 scopus 로고
    • Mittelmann H.D., and Roose D. (Eds), Birkhäuser, Charlottesville, VA
    • In: Mittelmann H.D., and Roose D. (Eds). Continuation Techniques and Bifurcation Problems. ISNM 92 (1990), Birkhäuser, Charlottesville, VA
    • (1990) ISNM , vol.92
  • 285
    • 0027110814 scopus 로고
    • A new polynomial time method for a linear complementarity problem
    • Mizuno S. A new polynomial time method for a linear complementarity problem. Math. Programming 56 (1992) 31-43
    • (1992) Math. Programming , vol.56 , pp. 31-43
    • Mizuno, S.1
  • 286
    • 0000836925 scopus 로고
    • On adaptive-step primal-dual interior-point algorithms for linear programming
    • to appear
    • to appear. Mizuno S., Todd M.J., and Ye Y. On adaptive-step primal-dual interior-point algorithms for linear programming. Math. Oper. Res. (1992)
    • (1992) Math. Oper. Res.
    • Mizuno, S.1    Todd, M.J.2    Ye, Y.3
  • 287
    • 0013496214 scopus 로고
    • Practical polynomial time algorithms for linear complementarity problems
    • Mizuno S., Yoshise A., and Kikuchi T. Practical polynomial time algorithms for linear complementarity problems. J. Oper. Res. Soc. Japan 32 (1989) 75-92
    • (1989) J. Oper. Res. Soc. Japan , vol.32 , pp. 75-92
    • Mizuno, S.1    Yoshise, A.2    Kikuchi, T.3
  • 288
    • 0024665752 scopus 로고
    • Interior path following primal-dual algorithms, I: Linear programming, II: Convex quadratic programming
    • Monteiro R.C., and Adler I. Interior path following primal-dual algorithms, I: Linear programming, II: Convex quadratic programming. Math. Programming 44 (1989) 27-66
    • (1989) Math. Programming , vol.44 , pp. 27-66
    • Monteiro, R.C.1    Adler, I.2
  • 289
    • 0000863468 scopus 로고
    • The calculation of turning points of nonlinear equations
    • Moore G., and Spence A. The calculation of turning points of nonlinear equations. SIAM J. Numer. Anal. 17 (1980) 567-576
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 567-576
    • Moore, G.1    Spence, A.2
  • 290
    • 38249043871 scopus 로고
    • A transformation to avoid solutions at infinity for polynomial systems
    • Morgan A.P. A transformation to avoid solutions at infinity for polynomial systems. Appl. Math. Comput. 18 (1986) 77-86
    • (1986) Appl. Math. Comput. , vol.18 , pp. 77-86
    • Morgan, A.P.1
  • 292
    • 0001733264 scopus 로고
    • A homotopy for solving general polynomial systems that respects m-homogeneous structures
    • Morgan A.P., and Sommese A.J. A homotopy for solving general polynomial systems that respects m-homogeneous structures. Appl. Math. Comput. 24 (1987) 101-113
    • (1987) Appl. Math. Comput. , vol.24 , pp. 101-113
    • Morgan, A.P.1    Sommese, A.J.2
  • 293
    • 0000749801 scopus 로고
    • Coefficient parameter polynomial continuation
    • Morgan A.P., and Sommese A.J. Coefficient parameter polynomial continuation. Appl. Math. Comput. 29 (1989) 123-160
    • (1989) Appl. Math. Comput. , vol.29 , pp. 123-160
    • Morgan, A.P.1    Sommese, A.J.2
  • 294
    • 34249955199 scopus 로고
    • Computing singular solutions to nonlinear analytic systems
    • Morgan A.P., Sommese A.J., and Wampler C.W. Computing singular solutions to nonlinear analytic systems. Numer. Math. 58 (1991) 669-684
    • (1991) Numer. Math. , vol.58 , pp. 669-684
    • Morgan, A.P.1    Sommese, A.J.2    Wampler, C.W.3
  • 295
  • 296
    • 21144479938 scopus 로고
    • A power series method for computing singular solutions to nonlinear analytic systems
    • Morgan A.P., Sommese A.J., and Wampler C.W. A power series method for computing singular solutions to nonlinear analytic systems. Numer. Math. 63 (1993) 391-409
    • (1993) Numer. Math. , vol.63 , pp. 391-409
    • Morgan, A.P.1    Sommese, A.J.2    Wampler, C.W.3
  • 297
    • 0024679842 scopus 로고
    • Finding all isolated solutions to polynomial systems using HOMPACK
    • Morgan A.P., Sommese A.J., and Watson L.T. Finding all isolated solutions to polynomial systems using HOMPACK. ACM Trans. Math. Software 15 (1989) 93-122
    • (1989) ACM Trans. Math. Software , vol.15 , pp. 93-122
    • Morgan, A.P.1    Sommese, A.J.2    Watson, L.T.3
  • 299
    • 52449145915 scopus 로고
    • Homotopy techniques in linear programming
    • Nazareth J.L. Homotopy techniques in linear programming. Algorithmica 1 (1986) 529-535
    • (1986) Algorithmica , vol.1 , pp. 529-535
    • Nazareth, J.L.1
  • 300
    • 0041893719 scopus 로고
    • The homotopy principle and algorithms for linear programming
    • Nazareth J.L. The homotopy principle and algorithms for linear programming. SIAM J. Optim. 1 (1991) 316-332
    • (1991) SIAM J. Optim. , vol.1 , pp. 316-332
    • Nazareth, J.L.1
  • 302
    • 0041392747 scopus 로고
    • The implementation of linear programming algorithms based on homotopies
    • Nazareth J.L. The implementation of linear programming algorithms based on homotopies. Algorithmica 15 (1994) 332-350
    • (1994) Algorithmica , vol.15 , pp. 332-350
    • Nazareth, J.L.1
  • 306
    • 0001354924 scopus 로고
    • Topologische Perturbationen beim globalen numerischen Studium nichtlinearer Eigenwert- und Verzweigungsprobleme
    • Peitgen H.-O. Topologische Perturbationen beim globalen numerischen Studium nichtlinearer Eigenwert- und Verzweigungsprobleme. Jahresber. Deutsch. Math.-Verein. 84 (1982) 107-162
    • (1982) Jahresber. Deutsch. Math.-Verein. , vol.84 , pp. 107-162
    • Peitgen, H.-O.1
  • 307
    • 0141902907 scopus 로고
    • The Leray-Schauder continuation method is a constructive element in the numerical study of nonlinear eigenvalue and bifurcation problems
    • Functional Differential Equations and Approximation of Fixed Points. Peitgen H.-O., and Walther H.-O. (Eds), Springer, Berlin
    • Peitgen H.-O., and Prüfer M. The Leray-Schauder continuation method is a constructive element in the numerical study of nonlinear eigenvalue and bifurcation problems. In: Peitgen H.-O., and Walther H.-O. (Eds). Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Math. 730 (1979), Springer, Berlin 326-409
    • (1979) Lecture Notes in Math. , vol.730 , pp. 326-409
    • Peitgen, H.-O.1    Prüfer, M.2
  • 308
    • 0020899909 scopus 로고
    • Global topological perturbations in the study of nonlinear eigenvalue problems
    • Peitgen H.-O., and Schmitt K. Global topological perturbations in the study of nonlinear eigenvalue problems. Math. Methods Appl. Sci. 5 (1983) 376-388
    • (1983) Math. Methods Appl. Sci. , vol.5 , pp. 376-388
    • Peitgen, H.-O.1    Schmitt, K.2
  • 309
    • 0000656883 scopus 로고
    • An ε--perturbation of Brouwer's definition of degree
    • Fixed Point Theory. Fadell E., and Fournier G. (Eds), Springer, Berlin
    • Peitgen H.-O., and Siegberg H.W. An ε--perturbation of Brouwer's definition of degree. In: Fadell E., and Fournier G. (Eds). Fixed Point Theory. Lecture Notes in Math. 886 (1981), Springer, Berlin 331-366
    • (1981) Lecture Notes in Math. , vol.886 , pp. 331-366
    • Peitgen, H.-O.1    Siegberg, H.W.2
  • 311
    • 70350643792 scopus 로고
    • Sur les Courbes Definé par une Équation Differentielle. I-IV
    • Gauthier-Villars, Berlin
    • Poincaré H. Sur les Courbes Definé par une Équation Differentielle. I-IV. Oeuvres I (1886), Gauthier-Villars, Berlin
    • (1886) Oeuvres , vol.I
    • Poincaré, H.1
  • 312
    • 34249832214 scopus 로고
    • A barrier function method for minimax problems
    • Polak E., Higgins J.E., and Mayne D.Q. A barrier function method for minimax problems. Math. Programming 54 (1992) 155-176
    • (1992) Math. Programming , vol.54 , pp. 155-176
    • Polak, E.1    Higgins, J.E.2    Mayne, D.Q.3
  • 314
    • 0022183447 scopus 로고
    • Computing simple bifurcation points using a minimally extended system of nonlinear equations
    • Pönisch G. Computing simple bifurcation points using a minimally extended system of nonlinear equations. Computing 35 (1985) 277-294
    • (1985) Computing , vol.35 , pp. 277-294
    • Pönisch, G.1
  • 315
    • 0040827848 scopus 로고
    • Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter
    • Pönisch G., and Schwetlick H. Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter. Computing 26 (1981) 107-121
    • (1981) Computing , vol.26 , pp. 107-121
    • Pönisch, G.1    Schwetlick, H.2
  • 316
    • 0040416113 scopus 로고
    • Ein überlinear konvergentes Verfahren zur Bestimmung von Rückkehrpunkten implizit definierter Raumkurven
    • Pönisch G., and Schwetlick H. Ein überlinear konvergentes Verfahren zur Bestimmung von Rückkehrpunkten implizit definierter Raumkurven. Numer. Math. 38 (1982) 455-466
    • (1982) Numer. Math. , vol.38 , pp. 455-466
    • Pönisch, G.1    Schwetlick, H.2
  • 317
    • 0023453048 scopus 로고
    • Bifurcation problems in nonlinear parametric programming
    • Poore A.B., and Tiahrt C.A. Bifurcation problems in nonlinear parametric programming. Math. Programming 39 (1987) 189-205
    • (1987) Math. Programming , vol.39 , pp. 189-205
    • Poore, A.B.1    Tiahrt, C.A.2
  • 318
    • 0000793680 scopus 로고
    • A bifurcation analysis of the nonlinear parametric programming problem
    • Poore A.B., and Tiahrt C.A. A bifurcation analysis of the nonlinear parametric programming problem. Math. Programming 47 (1990) 117-141
    • (1990) Math. Programming , vol.47 , pp. 117-141
    • Poore, A.B.1    Tiahrt, C.A.2
  • 319
    • 0002626122 scopus 로고
    • A Fortran subroutine for solving nonlinear algebraic equations
    • Rabinowitz P. (Ed), Gordon and Breach, Paris
    • Powell M.J.D. A Fortran subroutine for solving nonlinear algebraic equations. In: Rabinowitz P. (Ed). Numerical Methods for Nonlinear Algebraic Equations (1970), Gordon and Breach, Paris 115-161
    • (1970) Numerical Methods for Nonlinear Algebraic Equations , pp. 115-161
    • Powell, M.J.D.1
  • 320
    • 0002626123 scopus 로고
    • A hybrid method for nonlinear equations
    • Rabinowitz P. (Ed), Gordon and Breach, New York
    • Powell M.J.D. A hybrid method for nonlinear equations. In: Rabinowitz P. (Ed). Numerical Methods for Nonlinear Algebraic Equations (1970), Gordon and Breach, New York 87-114
    • (1970) Numerical Methods for Nonlinear Algebraic Equations , pp. 87-114
    • Powell, M.J.D.1
  • 321
    • 33846446220 scopus 로고
    • Restart procedures for the conjugate gradient method
    • Powell M.J.D. Restart procedures for the conjugate gradient method. Math. Programming 12 (1977) 241-254
    • (1977) Math. Programming , vol.12 , pp. 241-254
    • Powell, M.J.D.1
  • 322
    • 0009825171 scopus 로고
    • Characterization and computation of singular points with maximum rank deficiency
    • Rabier P.J., and Reddien G.W. Characterization and computation of singular points with maximum rank deficiency. SIAM J. Numer. Anal. 23 (1986) 1040-1051
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 1040-1051
    • Rabier, P.J.1    Reddien, G.W.2
  • 323
    • 36448974335 scopus 로고
    • Some global results for nonlinear eigenvalue problems
    • Rabinowitz P.H. Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7 (1971) 487-513
    • (1971) J. Funct. Anal. , vol.7 , pp. 487-513
    • Rabinowitz, P.H.1
  • 324
    • 0342814532 scopus 로고
    • An active set algorithm for tracing parametrized optima
    • Rakowska J., Haftka R.T., and Watson L.T. An active set algorithm for tracing parametrized optima. Struct. Optim. 3 (1991) 29-44
    • (1991) Struct. Optim. , vol.3 , pp. 29-44
    • Rakowska, J.1    Haftka, R.T.2    Watson, L.T.3
  • 325
    • 0022027268 scopus 로고
    • Solving generalized equations via homotopies
    • Reinoza A. Solving generalized equations via homotopies. Math. Programming 31 (1985) 307-320
    • (1985) Math. Programming , vol.31 , pp. 307-320
    • Reinoza, A.1
  • 326
    • 0022093773 scopus 로고
    • On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials
    • Renegar J. On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials. Math. Programming 32 (1985) 301-318
    • (1985) Math. Programming , vol.32 , pp. 301-318
    • Renegar, J.1
  • 327
    • 0023292476 scopus 로고
    • On the efficiency of Newton's method in approximating all zeros of systems of complex polynomials
    • Renegar J. On the efficiency of Newton's method in approximating all zeros of systems of complex polynomials. Math. Oper. Res. 12 (1987) 121-148
    • (1987) Math. Oper. Res. , vol.12 , pp. 121-148
    • Renegar, J.1
  • 328
    • 0023862337 scopus 로고
    • A polynomial-time algorithm, based on Newton's method, for linear programming
    • Renegar J. A polynomial-time algorithm, based on Newton's method, for linear programming. Math. Programming 40 (1988) 59-93
    • (1988) Math. Programming , vol.40 , pp. 59-93
    • Renegar, J.1
  • 329
    • 34250090502 scopus 로고
    • Rudiments of an average case complexity theory for piecewise-linear path following algorithms
    • Renegar J. Rudiments of an average case complexity theory for piecewise-linear path following algorithms. Math. Programming 40 (1988) 113-163
    • (1988) Math. Programming , vol.40 , pp. 113-163
    • Renegar, J.1
  • 330
    • 0026759893 scopus 로고
    • Unified complexity analysis for Newton LP methods
    • Renegar J., and Shub M. Unified complexity analysis for Newton LP methods. Math. Programming 53 (1992) 1-16
    • (1992) Math. Programming , vol.53 , pp. 1-16
    • Renegar, J.1    Shub, M.2
  • 331
    • 0040272580 scopus 로고
    • Numerical methods for a class of finite dimensional bifurcation problems
    • Rheinboldt W.C. Numerical methods for a class of finite dimensional bifurcation problems. SIAM J. Numer. Anal. 15 (1978) 1-11
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 1-11
    • Rheinboldt, W.C.1
  • 332
    • 0001509743 scopus 로고
    • Solution fields of nonlinear equations and continuation methods
    • Rheinboldt W.C. Solution fields of nonlinear equations and continuation methods. SIAM J. Numer. Anal. 17 (1980) 221-237
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 221-237
    • Rheinboldt, W.C.1
  • 333
    • 0011424547 scopus 로고
    • Numerical analysis of continuation methods for nonlinear structural problems
    • Rheinboldt W.C. Numerical analysis of continuation methods for nonlinear structural problems. Comput. & Structures 13 (1981) 103-113
    • (1981) Comput. & Structures , vol.13 , pp. 103-113
    • Rheinboldt, W.C.1
  • 335
    • 0009926071 scopus 로고
    • On a moving-frame algorithm and the triangulation of equilibrium manifolds
    • Bifurcation: Analysis, Algorithms, Applications. Küpper T., Seydel R., and Troger H. (Eds), Birkhäuser, New York
    • Rheinboldt W.C. On a moving-frame algorithm and the triangulation of equilibrium manifolds. In: Küpper T., Seydel R., and Troger H. (Eds). Bifurcation: Analysis, Algorithms, Applications. ISNM 79 (1987), Birkhäuser, New York 256-267
    • (1987) ISNM , vol.79 , pp. 256-267
    • Rheinboldt, W.C.1
  • 336
    • 38249029624 scopus 로고
    • On a theorem of S. Smale about Newton's method for analytic mappings
    • Rheinboldt W.C. On a theorem of S. Smale about Newton's method for analytic mappings. Appl. Math. Lett. 1 (1988) 69-72
    • (1988) Appl. Math. Lett. , vol.1 , pp. 69-72
    • Rheinboldt, W.C.1
  • 337
    • 0000256568 scopus 로고
    • On the computation of multi-dimensional solution manifolds of parametrized equations
    • Rheinboldt W.C. On the computation of multi-dimensional solution manifolds of parametrized equations. Numer. Math. 53 (1988) 165-182
    • (1988) Numer. Math. , vol.53 , pp. 165-182
    • Rheinboldt, W.C.1
  • 338
    • 84907916737 scopus 로고
    • On the theory and numerics of differential-algebraic equations
    • Light W. (Ed), Oxford Univ. Press, Basel
    • Rheinboldt W.C. On the theory and numerics of differential-algebraic equations. In: Light W. (Ed). Advances in Numerical Analysis (1992), Oxford Univ. Press, Basel 237-275
    • (1992) Advances in Numerical Analysis , pp. 237-275
    • Rheinboldt, W.C.1
  • 339
    • 0027574655 scopus 로고
    • On the sensitivity of solutions of parametrized equations
    • Rheinboldt W.C. On the sensitivity of solutions of parametrized equations. SIAM J. Numer. Anal. 30 (1993) 305-320
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 305-320
    • Rheinboldt, W.C.1
  • 340
    • 84976786620 scopus 로고
    • Algorithm 596: A program for a locally-parametrized continuation process
    • Rheinboldt W.C., and Burkardt J.V. Algorithm 596: A program for a locally-parametrized continuation process. ACM Trans. Math. Software 9 (1983) 236-241
    • (1983) ACM Trans. Math. Software , vol.9 , pp. 236-241
    • Rheinboldt, W.C.1    Burkardt, J.V.2
  • 342
    • 0001894464 scopus 로고
    • Aspects of continuation software
    • Continuation and Bifurcations: Numerical Techniques and Applications. Roose D., De Dier B., and Spence A. (Eds), Kluwer, Oxford, UK
    • Rheinboldt W.C., Roose D., and Seydel R. Aspects of continuation software. In: Roose D., De Dier B., and Spence A. (Eds). Continuation and Bifurcations: Numerical Techniques and Applications. NATO ASI Series C 313 (1990), Kluwer, Oxford, UK 261-268
    • (1990) NATO ASI Series C , vol.313 , pp. 261-268
    • Rheinboldt, W.C.1    Roose, D.2    Seydel, R.3
  • 343
    • 0002939936 scopus 로고
    • Generalized equations
    • Bachem A., Grötschel M., and Korte B. (Eds), Springer, Dordrecht
    • Robinson S.M. Generalized equations. In: Bachem A., Grötschel M., and Korte B. (Eds). Mathematical Programming - The State of the Art (1983), Springer, Dordrecht 346-367
    • (1983) Mathematical Programming - The State of the Art , pp. 346-367
    • Robinson, S.M.1
  • 344
    • 0020702702 scopus 로고
    • Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
    • Robinson S.M. Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity. Math. Programming Study 30 (1987) 45-66
    • (1987) Math. Programming Study , vol.30 , pp. 45-66
    • Robinson, S.M.1
  • 345
    • 70350681969 scopus 로고
    • Roos C., and Vial J.-P. (Eds), Mathematical Programming Society, North-Holland, Berlin
    • In: Roos C., and Vial J.-P. (Eds). Interior Point Methods for Linear Programming: Theory and Practice. Math. Programming 52 (1991), Mathematical Programming Society, North-Holland, Berlin
    • (1991) Math. Programming , vol.52
  • 346
    • 0005275159 scopus 로고
    • Roose D., de Dier B., and Spence A. (Eds), Kluwer, Amsterdam
    • In: Roose D., de Dier B., and Spence A. (Eds). Continuation and Bifurcations: Numerical Techniques and Applications. NATO ASI Series C 313 (1990), Kluwer, Amsterdam
    • (1990) NATO ASI Series C , vol.313
  • 347
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual method for solving nonsymmetric linear systems
    • Saad Y., and Schultz M. GMRES: A generalized minimal residual method for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comp. 7 (1986) 856-869
    • (1986) SIAM J. Sci. Statist. Comp. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.2
  • 348
    • 0040142880 scopus 로고
    • Lemke's algorithm and a special linear complementarity problem
    • Saigal R. Lemke's algorithm and a special linear complementarity problem. Oper. Res. 8 (1971) 201-208
    • (1971) Oper. Res. , vol.8 , pp. 201-208
    • Saigal, R.1
  • 349
    • 0016990201 scopus 로고
    • Extension of the generalized complementarity problem
    • Saigal R. Extension of the generalized complementarity problem. Math. Oper. Res. 1 (1976) 260-266
    • (1976) Math. Oper. Res. , vol.1 , pp. 260-266
    • Saigal, R.1
  • 350
    • 33646992754 scopus 로고
    • On the convergence rate of algorithms for solving equations that are based on methods of complementary pivoting
    • Saigal R. On the convergence rate of algorithms for solving equations that are based on methods of complementary pivoting. Math. Oper. Res. 2 (1977) 108-124
    • (1977) Math. Oper. Res. , vol.2 , pp. 108-124
    • Saigal, R.1
  • 351
    • 0018464969 scopus 로고
    • On piecewise linear approximations to smooth mappings
    • Saigal R. On piecewise linear approximations to smooth mappings. Math. Oper. Res. 4 (1979) 153-161
    • (1979) Math. Oper. Res. , vol.4 , pp. 153-161
    • Saigal, R.1
  • 352
    • 0021374334 scopus 로고
    • Computational complexity of a piecewise linear homotopy algorithm
    • Saigal R. Computational complexity of a piecewise linear homotopy algorithm. Math. Programming 28 (1984) 164-173
    • (1984) Math. Programming , vol.28 , pp. 164-173
    • Saigal, R.1
  • 353
    • 33646992093 scopus 로고
    • Efficient acceleration techniques for fixed point algorithms
    • Saigal R., and Todd M.J. Efficient acceleration techniques for fixed point algorithms. SIAM J. Numer. Anal. 15 (1978) 997-1007
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 997-1007
    • Saigal, R.1    Todd, M.J.2
  • 354
    • 33646993366 scopus 로고
    • On accelerating PL continuation algorithms by predictor-corrector methods
    • Saupe D. On accelerating PL continuation algorithms by predictor-corrector methods. Math. Programming 23 (1982) 87-110
    • (1982) Math. Programming , vol.23 , pp. 87-110
    • Saupe, D.1
  • 355
    • 0001310049 scopus 로고
    • The approximation of fixed points of a continuous mapping
    • Scarf H.E. The approximation of fixed points of a continuous mapping. SIAM J. Appl. Math. 15 (1967) 1328-1343
    • (1967) SIAM J. Appl. Math. , vol.15 , pp. 1328-1343
    • Scarf, H.E.1
  • 356
    • 84919056567 scopus 로고
    • Algorithms for finite-dimensional turning point problems from viewpoint to relationships with constrained optimization methods
    • Küpper T., Mittelmann H., and Weber H. (Eds), Birkhäuser, Dordrecht
    • Schwetlick H. Algorithms for finite-dimensional turning point problems from viewpoint to relationships with constrained optimization methods. In: Küpper T., Mittelmann H., and Weber H. (Eds). Numerical Methods for Bifurcation Problems (1984), Birkhäuser, Dordrecht 459-479
    • (1984) Numerical Methods for Bifurcation Problems , pp. 459-479
    • Schwetlick, H.1
  • 357
    • 33646992543 scopus 로고
    • Effective methods for computing turning points of curves implicitly defined by nonlinear equations
    • Computational Mathematics. Wakulicz A. (Ed), PWN, Basel
    • Schwetlick H. Effective methods for computing turning points of curves implicitly defined by nonlinear equations. In: Wakulicz A. (Ed). Computational Mathematics. Banach Center Publications 13 (1984), PWN, Basel 623-645
    • (1984) Banach Center Publications , vol.13 , pp. 623-645
    • Schwetlick, H.1
  • 358
    • 0023599320 scopus 로고
    • Higher order predictors and adaptive stepsize control in path following algorithms
    • Schwetlick H., and Cleve J. Higher order predictors and adaptive stepsize control in path following algorithms. SIAM J. Numer. Anal. 24 (1987) 1382-1393
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1382-1393
    • Schwetlick, H.1    Cleve, J.2
  • 359
    • 0025920032 scopus 로고
    • Nonlinear analysis in process design
    • Seider W.D., Brengel D.D., and Widagdo S. Nonlinear analysis in process design. AIChE J. 37 (1991) 1-38
    • (1991) AIChE J. , vol.37 , pp. 1-38
    • Seider, W.D.1    Brengel, D.D.2    Widagdo, S.3
  • 360
    • 0003688588 scopus 로고
    • A continuation method for normal maps
    • Department of Industrial Engineering, University of Wisconsin-Madison, Warsaw
    • Sellami H., and Robinson S.M. A continuation method for normal maps. Technical Report 93-8 (1993), Department of Industrial Engineering, University of Wisconsin-Madison, Warsaw
    • (1993) Technical Report 93-8
    • Sellami, H.1    Robinson, S.M.2
  • 361
    • 0001621239 scopus 로고
    • Linear Representations of Finite Groups
    • Springer, Madison, WI
    • Serre J.-P. Linear Representations of Finite Groups. Graduate Texts in Mathematics 42 (1977), Springer, Madison, WI
    • (1977) Graduate Texts in Mathematics , vol.42
    • Serre, J.-P.1
  • 362
    • 0002274823 scopus 로고
    • Numerical computation of branch points of nonlinear equations
    • Seydel R. Numerical computation of branch points of nonlinear equations. Numer. Math. 33 (1979) 339-352
    • (1979) Numer. Math. , vol.33 , pp. 339-352
    • Seydel, R.1
  • 365
    • 0001608607 scopus 로고
    • On detecting stationary bifurcations
    • Seydel R. On detecting stationary bifurcations. Internat. J. Bifurcation Chaos 1 (1991) 335-337
    • (1991) Internat. J. Bifurcation Chaos , vol.1 , pp. 335-337
    • Seydel, R.1
  • 366
    • 70350653895 scopus 로고
    • Seydel R., Schneider F.W., Küpper T., and Troger H. (Eds), Birkhäuser, Germany
    • In: Seydel R., Schneider F.W., Küpper T., and Troger H. (Eds). Bifurcation and Chaos: Analysis, Algorithms, Applications. ISNM 97 (1991), Birkhäuser, Germany
    • (1991) ISNM , vol.97
  • 368
    • 0000183805 scopus 로고
    • A note on the Lemke-Howson algorithm
    • Pivoting and Extensions: In Honor of A.W. Tucker. Balinski M.L. (Ed), North-Holland, San Francisco
    • Shapley L.S. A note on the Lemke-Howson algorithm. In: Balinski M.L. (Ed). Pivoting and Extensions: In Honor of A.W. Tucker. Math. Programming Study 1 (1974), North-Holland, San Francisco 175-189
    • (1974) Math. Programming Study , vol.1 , pp. 175-189
    • Shapley, L.S.1
  • 370
    • 0027641824 scopus 로고
    • Stabilization of unstable procedures: The recursive projection method
    • Shroff G.M., and Keller H.B. Stabilization of unstable procedures: The recursive projection method. SIAM J. Numer. Anal. 30 (1993) 1099-1120
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1099-1120
    • Shroff, G.M.1    Keller, H.B.2
  • 371
    • 70350690638 scopus 로고
    • Complexity of Bezout's theorem, I: Geometric aspects
    • Shub M., and Smale S. Complexity of Bezout's theorem, I: Geometric aspects. IBM Research Report (1991)
    • (1991) IBM Research Report
    • Shub, M.1    Smale, S.2
  • 372
    • 70350652113 scopus 로고
    • Numerical integration over implicitly defined curves
    • Colorado State University, New York
    • Siyyam H.I. Numerical integration over implicitly defined curves. PhD thesis (1994), Colorado State University, New York
    • (1994) PhD thesis
    • Siyyam, H.I.1
  • 373
    • 49549130863 scopus 로고
    • A convergent process of price adjustement and global Newton methods
    • Smale S. A convergent process of price adjustement and global Newton methods. J. Math. Econom 3 (1976) 1-14
    • (1976) J. Math. Econom , vol.3 , pp. 1-14
    • Smale, S.1
  • 375
    • 0001292818 scopus 로고
    • An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming
    • Springer, New York
    • Sonnevend G. An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming. Lecture Notes in Control and Information Sciences 84 (1985), Springer, New York 866-876
    • (1985) Lecture Notes in Control and Information Sciences , vol.84 , pp. 866-876
    • Sonnevend, G.1
  • 376
    • 0012308688 scopus 로고
    • On the complexity of following the central path of linear programs by linear extrapolation
    • Sonnevend G., Stoer J., and Zhao G. On the complexity of following the central path of linear programs by linear extrapolation. Methods Oper. Res. 63 (1989) 19-31
    • (1989) Methods Oper. Res. , vol.63 , pp. 19-31
    • Sonnevend, G.1    Stoer, J.2    Zhao, G.3
  • 377
    • 34249921867 scopus 로고
    • On the complexity of following the central path of linear programs by linear extrapolation II
    • Ser. B. Interior Point Methods for Linear Programming: Theory and Practice. Roos C., and Vial J.-P. (Eds), Mathematical Programming Society, North-Holland, New York
    • Ser. B. Sonnevend G., Stoer J., and Zhao G. On the complexity of following the central path of linear programs by linear extrapolation II. In: Roos C., and Vial J.-P. (Eds). Interior Point Methods for Linear Programming: Theory and Practice. Math. Programming 52 (1991), Mathematical Programming Society, North-Holland, New York 527-553
    • (1991) Math. Programming , vol.52 , pp. 527-553
    • Sonnevend, G.1    Stoer, J.2    Zhao, G.3
  • 378
    • 70350688031 scopus 로고
    • Two applications of group characters to the solution of boundary-value problems
    • Stiefel E. Two applications of group characters to the solution of boundary-value problems. J. Res. Nat. Bur. Standards 6 (1952) 424-427
    • (1952) J. Res. Nat. Bur. Standards , vol.6 , pp. 424-427
    • Stiefel, E.1
  • 380
    • 0005124950 scopus 로고
    • Solution of large linear systems of equations by conjugate gradient type methods
    • Bachem A., Grötschel M., and Korte B. (Eds), Springer, Stuttgart
    • Stoer J. Solution of large linear systems of equations by conjugate gradient type methods. In: Bachem A., Grötschel M., and Korte B. (Eds). Mathematical Programming: The State of the Art (1983), Springer, Stuttgart 540-565
    • (1983) Mathematical Programming: The State of the Art , pp. 540-565
    • Stoer, J.1
  • 382
    • 0000156969 scopus 로고
    • A simplicial algorithm for stationary point problems on polytopes
    • Talman A.J.J., and Yamamoto Y. A simplicial algorithm for stationary point problems on polytopes. Math. Oper. Res. 14 (1989) 383-399
    • (1989) Math. Oper. Res. , vol.14 , pp. 383-399
    • Talman, A.J.J.1    Yamamoto, Y.2
  • 383
    • 0000115006 scopus 로고
    • Continuous Newton-Raphson method for solving an underdetermined system of nonlinear equations
    • Tanabe K. Continuous Newton-Raphson method for solving an underdetermined system of nonlinear equations. Nonlinear Anal. 3 (1979) 495-503
    • (1979) Nonlinear Anal. , vol.3 , pp. 495-503
    • Tanabe, K.1
  • 384
    • 0041309100 scopus 로고
    • A generalization of the discrete Fourier transformation
    • Exploiting Symmetry in Applied and Numerical Analysis. Allgower E.L., Georg K., and Miranda R. (Eds), American Mathematical Society, Englewood Cliffs, NJ
    • Tausch J. A generalization of the discrete Fourier transformation. In: Allgower E.L., Georg K., and Miranda R. (Eds). Exploiting Symmetry in Applied and Numerical Analysis. Lectures in Applied Mathematics 29 (1993), American Mathematical Society, Englewood Cliffs, NJ 405-412
    • (1993) Lectures in Applied Mathematics , vol.29 , pp. 405-412
    • Tausch, J.1
  • 385
    • 0003222289 scopus 로고
    • The Computation of Fixed Points and Applications
    • Springer, Providence, RI
    • Todd M.J. The Computation of Fixed Points and Applications. Lecture Notes in Economics and Mathematical Systems 124 (1976), Springer, Providence, RI
    • (1976) Lecture Notes in Economics and Mathematical Systems , vol.124
    • Todd, M.J.1
  • 386
    • 33646993196 scopus 로고
    • Extensions of Lemke's algorithm for the linear complementarity problem
    • Todd M.J. Extensions of Lemke's algorithm for the linear complementarity problem. J. Optim. Theory Appl. 20 (1976) 397-416
    • (1976) J. Optim. Theory Appl. , vol.20 , pp. 397-416
    • Todd, M.J.1
  • 387
    • 0016916811 scopus 로고
    • Orientation in complementary pivot algorithms
    • Todd M.J. Orientation in complementary pivot algorithms. Math. Oper. Res. 1 (1976) 54-66
    • (1976) Math. Oper. Res. , vol.1 , pp. 54-66
    • Todd, M.J.1
  • 388
    • 84932304399 scopus 로고
    • Fixed-point algorithms that allow restarting without extra dimension
    • Cornell University, Berlin
    • Todd M.J. Fixed-point algorithms that allow restarting without extra dimension. Technical Report (1978), Cornell University, Berlin
    • (1978) Technical Report
    • Todd, M.J.1
  • 389
    • 33646993183 scopus 로고
    • On the Jacobian of a function at a zero computed by a fixed point algorithm
    • Todd M.J. On the Jacobian of a function at a zero computed by a fixed point algorithm. Math. Oper. Res. 3 (1978) 126-132
    • (1978) Math. Oper. Res. , vol.3 , pp. 126-132
    • Todd, M.J.1
  • 390
    • 33646993498 scopus 로고
    • A quadratically convergent fixed point algorithm for economic equilibria and linearly constrained optimization
    • Todd M.J. A quadratically convergent fixed point algorithm for economic equilibria and linearly constrained optimization. Math. Programming 18 (1980) 111-126
    • (1980) Math. Programming , vol.18 , pp. 111-126
    • Todd, M.J.1
  • 391
    • 70350681970 scopus 로고
    • PLALGO: A FORTRAN implementation of a piecewise-linear homotopy algorithm for solving systems of nonlinear equations
    • Cornell University, Ithaca, NY
    • Todd M.J. PLALGO: A FORTRAN implementation of a piecewise-linear homotopy algorithm for solving systems of nonlinear equations. School of Operations Research and Industrial Engineering (1981), Cornell University, Ithaca, NY
    • (1981) School of Operations Research and Industrial Engineering
    • Todd, M.J.1
  • 392
    • 0020192982 scopus 로고
    • On the computational complexity of piecewise-linear homotopy algorithms
    • Todd M.J. On the computational complexity of piecewise-linear homotopy algorithms. Math. Programming 24 (1982) 216-224
    • (1982) Math. Programming , vol.24 , pp. 216-224
    • Todd, M.J.1
  • 393
    • 0022739464 scopus 로고
    • Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems
    • Todd M.J. Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems. Math. Programming 35 (1986) 173-192
    • (1986) Math. Programming , vol.35 , pp. 173-192
    • Todd, M.J.1
  • 394
    • 0002665004 scopus 로고
    • Recent developments and new directions in linear programming
    • Iri N., and Tanabe K. (Eds), Kluwer, Ithaca, NY
    • Todd M.J. Recent developments and new directions in linear programming. In: Iri N., and Tanabe K. (Eds). Mathematical Programming, Recent Developments and Applications (1989), Kluwer, Ithaca, NY 109-157
    • (1989) Mathematical Programming, Recent Developments and Applications , pp. 109-157
    • Todd, M.J.1
  • 395
    • 0021190976 scopus 로고
    • Tracing solution curves of nonlinear equations with sharp turning points
    • Ushida A., and Chua L.O. Tracing solution curves of nonlinear equations with sharp turning points. Internat. J. Circuit Theory Appl. 12 (1984) 1-21
    • (1984) Internat. J. Circuit Theory Appl. , vol.12 , pp. 1-21
    • Ushida, A.1    Chua, L.O.2
  • 396
    • 0025446911 scopus 로고
    • 1.5n)L) arithmetic operations
    • 1.5n)L) arithmetic operations. Math. Programming 47 (1990) 175-202
    • (1990) Math. Programming , vol.47 , pp. 175-202
    • Vaidya, P.M.1
  • 398
    • 0018495053 scopus 로고
    • A restart algorithm for computing fixed points without an extra dimension
    • Van der Laan G., and Talman A.J.J. A restart algorithm for computing fixed points without an extra dimension. Math. Programming 17 (1979) 74-84
    • (1979) Math. Programming , vol.17 , pp. 74-84
    • Van der Laan, G.1    Talman, A.J.J.2
  • 399
    • 0141902920 scopus 로고
    • An improvement of fixed point algorithms by using a good triangulation
    • Van der Laan G., and Talman A.J.J. An improvement of fixed point algorithms by using a good triangulation. Math. Programming 18 (1980) 274-285
    • (1980) Math. Programming , vol.18 , pp. 274-285
    • Van der Laan, G.1    Talman, A.J.J.2
  • 401
    • 0003301233 scopus 로고
    • Computational Frameworks for the Fast Fourier Transform
    • SIAM, New York
    • Van Loan C. Computational Frameworks for the Fast Fourier Transform. Frontiers in Applied Mathematics 10 (1992), SIAM, New York
    • (1992) Frontiers in Applied Mathematics , vol.10
    • Van Loan, C.1
  • 402
    • 84968474149 scopus 로고
    • Proof of a conjectured asymptotic expansion for the approximation of surface integrals
    • Verlinden P., and Cools R. Proof of a conjectured asymptotic expansion for the approximation of surface integrals. Math. Comp. 63 (1994) 717-725
    • (1994) Math. Comp. , vol.63 , pp. 717-725
    • Verlinden, P.1    Cools, R.2
  • 403
    • 70350697745 scopus 로고
    • Solving very deficient systems of polynomial equations by implicit elimination
    • Katholieke Universiteit Leuven, Department of Computing Science, Philadelphia, PA
    • Verlinden P., and Haegemans A. Solving very deficient systems of polynomial equations by implicit elimination. Report TW 207 (1994), Katholieke Universiteit Leuven, Department of Computing Science, Philadelphia, PA
    • (1994) Report TW 207
    • Verlinden, P.1    Haegemans, A.2
  • 404
    • 21144472893 scopus 로고
    • Nonlinear reduction for solving deficient polynomial systems by continuation methods
    • Verschelde J., and Cools R. Nonlinear reduction for solving deficient polynomial systems by continuation methods. Numer. Math. 63 (1992) 263-282
    • (1992) Numer. Math. , vol.63 , pp. 263-282
    • Verschelde, J.1    Cools, R.2
  • 408
    • 0027574654 scopus 로고
    • The GBQ-algorithm for constructing start systems of homotopies for polynomial systems
    • Verschelde J., and Haegemans A. The GBQ-algorithm for constructing start systems of homotopies for polynomial systems. SIAM J. Numer. Anal. 30 (1993) 583-594
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 583-594
    • Verschelde, J.1    Haegemans, A.2
  • 409
    • 0028518349 scopus 로고
    • Homotopies for solving polynomial systems within a bounded domain
    • Verschelde J., and Haegemans A. Homotopies for solving polynomial systems within a bounded domain. Theoret. Comput. Sci. 133 (1994) 165-185
    • (1994) Theoret. Comput. Sci. , vol.133 , pp. 165-185
    • Verschelde, J.1    Haegemans, A.2
  • 410
    • 0028449799 scopus 로고
    • Homotopies exploiting Newton polytopes for solving sparse polynomial systems
    • Verschelde J., Verlinden P., and Cools R. Homotopies exploiting Newton polytopes for solving sparse polynomial systems. SIAM J. Numer. Anal. 31 (1994) 915-930
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 915-930
    • Verschelde, J.1    Verlinden, P.2    Cools, R.3
  • 411
    • 0000199896 scopus 로고
    • Newton-like methods for underdetermined systems
    • Computational Solution of Nonlinear Systems of Equations. Allgower E.L., and Georg K. (Eds), American Mathematical Society, Leuven, Belgium
    • Walker H.F. Newton-like methods for underdetermined systems. In: Allgower E.L., and Georg K. (Eds). Computational Solution of Nonlinear Systems of Equations. Lectures in Applied Mathematics 26 (1990), American Mathematical Society, Leuven, Belgium 679-700
    • (1990) Lectures in Applied Mathematics , vol.26 , pp. 679-700
    • Walker, H.F.1
  • 412
    • 0025957943 scopus 로고
    • Solving the 6R inverse position problem using a generic-case solution methodology
    • Wampler C.W., and Morgan A.P. Solving the 6R inverse position problem using a generic-case solution methodology. Mech. Mach. Theory 26 (1991) 91-106
    • (1991) Mech. Mach. Theory , vol.26 , pp. 91-106
    • Wampler, C.W.1    Morgan, A.P.2
  • 413
    • 84988473168 scopus 로고
    • Numerical continuation methods for solving polynomial systems arising in kinematics
    • Wampler C.W., Morgan A.P., and Sommese A.J. Numerical continuation methods for solving polynomial systems arising in kinematics. ASME J. Design 112 (1990) 59-68
    • (1990) ASME J. Design , vol.112 , pp. 59-68
    • Wampler, C.W.1    Morgan, A.P.2    Sommese, A.J.3
  • 414
    • 0026822964 scopus 로고
    • Complete solution of the nine-point path synthesis problem for four-bar linkages
    • Wampler C.W., Morgan A.P., and Sommese A.J. Complete solution of the nine-point path synthesis problem for four-bar linkages. ASME J. Mech. Design 114 (1992) 153-159
    • (1992) ASME J. Mech. Design , vol.114 , pp. 153-159
    • Wampler, C.W.1    Morgan, A.P.2    Sommese, A.J.3
  • 415
    • 0021452861 scopus 로고
    • Isospectral flows
    • Watkins D.S. Isospectral flows. SIAM Rev. 26 (1984) 379-391
    • (1984) SIAM Rev. , vol.26 , pp. 379-391
    • Watkins, D.S.1
  • 416
    • 0023415939 scopus 로고
    • HOMPACK: A suite of codes for globally convergent homotopy algorithms
    • Watson L.T., Billups S.C., and Morgan A.P. HOMPACK: A suite of codes for globally convergent homotopy algorithms. ACM Trans. Math. Software 13 (1987) 281-310
    • (1987) ACM Trans. Math. Software , vol.13 , pp. 281-310
    • Watson, L.T.1    Billups, S.C.2    Morgan, A.P.3
  • 417
    • 84919155890 scopus 로고
    • A review of continuation methods and their application to separations problems
    • Wayburn T.L. A review of continuation methods and their application to separations problems. AIChE Comput. Sys. Tech. 11 (1982) 8-22
    • (1982) AIChE Comput. Sys. Tech. , vol.11 , pp. 8-22
    • Wayburn, T.L.1
  • 418
    • 0023241048 scopus 로고
    • Homotopy continuation methods for computer-aided process design
    • Wayburn T.L., and Seader J.D. Homotopy continuation methods for computer-aided process design. Comput. Chem. Engrg. 11 (1987) 7-25
    • (1987) Comput. Chem. Engrg. , vol.11 , pp. 7-25
    • Wayburn, T.L.1    Seader, J.D.2
  • 419
    • 0003888709 scopus 로고
    • On the numerical approximation of secondary bifurcation problems
    • Numerical Solution of Nonlinear Equations. Allgower E.L., Glashoff K., and Peitgen H.-O. (Eds), Springer, Providence, RI
    • Weber H. On the numerical approximation of secondary bifurcation problems. In: Allgower E.L., Glashoff K., and Peitgen H.-O. (Eds). Numerical Solution of Nonlinear Equations. Lecture Notes in Math. 878 (1981), Springer, Providence, RI 407-425
    • (1981) Lecture Notes in Math. , vol.878 , pp. 407-425
    • Weber, H.1
  • 420
    • 0010717668 scopus 로고
    • Test functions for bifurcation points and Hopf points in problems with symmetries
    • Bifurcation and Symmetry. Allgower E.L., Böhmer K., and Golubitsky M. (Eds), Birkhäuser, New York
    • Werner B. Test functions for bifurcation points and Hopf points in problems with symmetries. In: Allgower E.L., Böhmer K., and Golubitsky M. (Eds). Bifurcation and Symmetry. ISNM 104 (1992), Birkhäuser, New York 317-327
    • (1992) ISNM , vol.104 , pp. 317-327
    • Werner, B.1
  • 421
    • 0021418315 scopus 로고
    • The computation of symmetry-breaking bifurcation points
    • Werner B., and Spence A. The computation of symmetry-breaking bifurcation points. SIAM J. Numer. Anal. 21 (1984) 388-399
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 388-399
    • Werner, B.1    Spence, A.2
  • 422
    • 0347987251 scopus 로고
    • Preprint, Colorado State University, Basel
    • 3 (1990), Colorado State University, Basel
    • (1990) 3
    • Widmann, R.1
  • 424
    • 0023091554 scopus 로고
    • A bifurcation study of laminar flow in a curved rectangular cross-section
    • Winters K.H. A bifurcation study of laminar flow in a curved rectangular cross-section. J. Fluid Mech. 180 (1987) 343-369
    • (1987) J. Fluid Mech. , vol.180 , pp. 343-369
    • Winters, K.H.1
  • 425
    • 0026413022 scopus 로고
    • Bifurcation and stability: A computational approach
    • Winters K.H. Bifurcation and stability: A computational approach. Comput. Phys. Commun. 65 (1991) 299-309
    • (1991) Comput. Phys. Commun. , vol.65 , pp. 299-309
    • Winters, K.H.1
  • 426
    • 0022145689 scopus 로고
    • The prediction of critical points for thermal explosions in a finite volume
    • Winters K.H., and K.A. The prediction of critical points for thermal explosions in a finite volume. Combust. Flame 62 (1985) 13-20
    • (1985) Combust. Flame , vol.62 , pp. 13-20
    • Winters, K.H.1
  • 427
    • 0041296573 scopus 로고
    • The prediction of instabilities using bifurcation theory
    • Lewis R.W., Hinton E.P., Bettess P., and Schrefler B.A. (Eds), Wiley
    • Winters K.H., Cliffe K.A., and Jackson C.P. The prediction of instabilities using bifurcation theory. In: Lewis R.W., Hinton E.P., Bettess P., and Schrefler B.A. (Eds). Numerical Methods for Transient and Coupled Problems (1987), Wiley 179-198
    • (1987) Numerical Methods for Transient and Coupled Problems , pp. 179-198
    • Winters, K.H.1    Cliffe, K.A.2    Jackson, C.P.3
  • 428
    • 44949291581 scopus 로고
    • Tracking bifurcating solutions of a model biological pattern generator
    • Winters K.H., Myerscough M.R., and Maini P.K. Tracking bifurcating solutions of a model biological pattern generator. Impact Comput. Sci. Eng. 2 (1990) 355-371
    • (1990) Impact Comput. Sci. Eng. , vol.2 , pp. 355-371
    • Winters, K.H.1    Myerscough, M.R.2    Maini, P.K.3
  • 429
    • 0019591032 scopus 로고
    • The octahedral algorithm, a new simplicial fixed point algorithm
    • Wright A.H. The octahedral algorithm, a new simplicial fixed point algorithm. Math. Programming 21 (1981) 47-69
    • (1981) Math. Programming , vol.21 , pp. 47-69
    • Wright, A.H.1
  • 430
    • 84966201471 scopus 로고
    • Finding all solutions to a system of polynomial equations
    • Wright A.H. Finding all solutions to a system of polynomial equations. Math. Comp 44 (1985) 125-133
    • (1985) Math. Comp , vol.44 , pp. 125-133
    • Wright, A.H.1
  • 431
    • 84971922797 scopus 로고
    • Interior methods for constrained optimization
    • Wright M.H. Interior methods for constrained optimization. Acta Numer. 1 (1992) 341-407
    • (1992) Acta Numer. , vol.1 , pp. 341-407
    • Wright, M.H.1
  • 432
    • 0040145940 scopus 로고
    • A direct method for computing higher order folds
    • Yang Z.-H., and Keller H.B. A direct method for computing higher order folds. SIAM J. Sci. Statist. Comput. 7 (1986) 351-361
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 351-361
    • Yang, Z.-H.1    Keller, H.B.2
  • 433
    • 34250078832 scopus 로고
    • A quadratically convergent O(√nL)-iteration algorithm for linear programming
    • Ye Y., Güler O., Tapia R.A., and Zhang Y. A quadratically convergent O(√nL)-iteration algorithm for linear programming. Math. Programming 59 (1991) 151-162
    • (1991) Math. Programming , vol.59 , pp. 151-162
    • Ye, Y.1    Güler, O.2    Tapia, R.A.3    Zhang, Y.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.