메뉴 건너뛰기




Volumn 123, Issue 1-2, 2000, Pages 447-465

Symbiosis between linear algebra and optimization

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; POLES AND ZEROS; QUADRATIC PROGRAMMING;

EID: 0034319857     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00408-8     Document Type: Article
Times cited : (5)

References (97)
  • 1
    • 0000728112 scopus 로고    scopus 로고
    • Implementation of interior point methods for large scale linear programs
    • T. Terlaky. Boston: Kluwer Academic Publishers
    • Andersen E.D., Gondzio J., Mészáros C., Xu X. Implementation of interior point methods for large scale linear programs. Terlaky T. Interior Point Methods of Mathematical Programming. 1996;189-252 Kluwer Academic Publishers, Boston.
    • (1996) Interior Point Methods of Mathematical Programming , pp. 189-252
    • Andersen, E.D.1    Gondzio, J.2    Mészáros, C.3    Xu, X.4
  • 3
    • 0030247572 scopus 로고    scopus 로고
    • A modified Schur-complement method for handling dense columns in interior point methods for linear programming
    • Andersen K.D. A modified Schur-complement method for handling dense columns in interior point methods for linear programming. ACM Trans. Math. Software. 22:1996;348-356.
    • (1996) ACM Trans. Math. Software , vol.22 , pp. 348-356
    • Andersen, K.D.1
  • 4
    • 0000015959 scopus 로고
    • Solving sparse linear systems with sparse backward error
    • Arioli M., Demmel J.W., Duff I.S. Solving sparse linear systems with sparse backward error. SIAM J. Matrix Anal. Appl. 10:1989;165-190.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 165-190
    • Arioli, M.1    Demmel, J.W.2    Duff, I.S.3
  • 5
    • 0000645096 scopus 로고
    • A stablization of the simplex method
    • Bartels R.H. A stablization of the simplex method. Numer. Math. 16:1971;414-434.
    • (1971) Numer. Math. , vol.16 , pp. 414-434
    • Bartels, R.H.1
  • 6
    • 0001637146 scopus 로고
    • The Simplex method of linear programming using LU decomposition
    • Bartels R.H., Golub G.H. The Simplex method of linear programming using LU decomposition. Comm. ACM. 12:1969;266-268.
    • (1969) Comm. ACM , vol.12 , pp. 266-268
    • Bartels, R.H.1    Golub, G.H.2
  • 7
    • 0006910070 scopus 로고    scopus 로고
    • Computing gradients in large-scale optimization using automatic differentiation
    • Bischof C., Bouaricha A., Khademi P., Moré J. Computing gradients in large-scale optimization using automatic differentiation. INFORMS J. Comput. 9:1997;185-194.
    • (1997) INFORMS J. Comput. , vol.9 , pp. 185-194
    • Bischof, C.1    Bouaricha, A.2    Khademi, P.3    Moré, J.4
  • 9
    • 0001330034 scopus 로고
    • Algorithms for confluent Vandermonde systems
    • Å. Björck, T. Elfving, Algorithms for confluent Vandermonde systems, Numer. Math. 21 (1973) 130-137.
    • (1973) Numer. Math. , vol.21 , pp. 130-137
    • Björck, Å.1    Elfving, T.2
  • 10
    • 0001688779 scopus 로고
    • Loss and recapture of orthogonality in the modified Gram-Schmidt algorithm
    • Å. Björck, C.C. Paige, Loss and recapture of orthogonality in the modified Gram-Schmidt algorithm, SIAM J. Matrix Anal. Appl. 13 (1992) 176-190.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 176-190
    • Björck, Å.1    Paige, C.C.2
  • 11
    • 84968468488 scopus 로고
    • Solution of Vandermonde system of equations
    • Å. Björck, V. Pereyra, Solution of Vandermonde system of equations, Math. Comp. 24 (1970) 893-903.
    • (1970) Math. Comp. , vol.24 , pp. 893-903
    • Björck, Å.1    Pereyra, V.2
  • 12
    • 44649149897 scopus 로고
    • Sequential quadratic programming
    • Boggs P.T., Tolle J.W. Sequential quadratic programming. Acta Numerica. 4:1995;1-51.
    • (1995) Acta Numerica , vol.4 , pp. 1-51
    • Boggs, P.T.1    Tolle, J.W.2
  • 14
    • 0015200767 scopus 로고
    • Direct methods for solving symmetric indefinite systems of linear equations
    • Bunch J.R., Parlett B.N. Direct methods for solving symmetric indefinite systems of linear equations. SIAM J. Numer. Anal. 8:1971;639-655.
    • (1971) SIAM J. Numer. Anal. , vol.8 , pp. 639-655
    • Bunch, J.R.1    Parlett, B.N.2
  • 15
    • 27144489164 scopus 로고    scopus 로고
    • A tutorial on support vector machines for pattern recognition
    • Burges C.J.C. A tutorial on support vector machines for pattern recognition. Data Mining Knowledge Discovery. 2:1998;121-167.
    • (1998) Data Mining Knowledge Discovery , vol.2 , pp. 121-167
    • Burges, C.J.C.1
  • 16
    • 0027606562 scopus 로고
    • An interior point method for quadratic programs based on conjugate projected gradients
    • Carpenter T.J., Shanno D.F. An interior point method for quadratic programs based on conjugate projected gradients. Comput. Optim. Appl. 2:1993;5-28.
    • (1993) Comput. Optim. Appl. , vol.2 , pp. 5-28
    • Carpenter, T.J.1    Shanno, D.F.2
  • 17
    • 0000439725 scopus 로고
    • Row-action methods for huge and sparse systems and their applications
    • Censor Y. Row-action methods for huge and sparse systems and their applications. SIAM Rev. 23:1981;444-466.
    • (1981) SIAM Rev. , vol.23 , pp. 444-466
    • Censor, Y.1
  • 21
    • 0040354312 scopus 로고    scopus 로고
    • Methods for nonlinear constraints in optimization calculations
    • I.S. Duff, & G.A. Watson. Oxford, England: Clarendon Press
    • Conn A.R., Gould N.I.M., Toint P.L. Methods for nonlinear constraints in optimization calculations. Duff I.S., Watson G.A. The State of the Art in Numerical Analysis. 1997;363-390 Clarendon Press, Oxford, England.
    • (1997) The State of the Art in Numerical Analysis , pp. 363-390
    • Conn, A.R.1    Gould, N.I.M.2    Toint, P.L.3
  • 23
    • 0019380732 scopus 로고
    • The least squares solution of overdetermined linear equations having band or augmented band structure
    • Cox M.G. The least squares solution of overdetermined linear equations having band or augmented band structure. IMA J. Numer. Anal. 1:1981;3-22.
    • (1981) IMA J. Numer. Anal. , vol.1 , pp. 3-22
    • Cox, M.G.1
  • 24
    • 0000176577 scopus 로고
    • Fast Toeplitz orthogonalization using inner products
    • Cybenko G. Fast Toeplitz orthogonalization using inner products. SIAM J. Sci. Statist. Comput. 8:1987;734-740.
    • (1987) SIAM J. Sci. Statist. Comput. , vol.8 , pp. 734-740
    • Cybenko, G.1
  • 27
    • 0002282066 scopus 로고
    • Fast QR factorization of Vandermonde matrices
    • Demeure C.J. Fast QR factorization of Vandermonde matrices. Linear Algebra Appl. 122(3) / 4:1989;165-194.
    • (1989) Linear Algebra Appl. , vol.122 , Issue.3-4 , pp. 165-194
    • Demeure, C.J.1
  • 28
    • 0002663672 scopus 로고
    • Quasi-Newton methods, motivation and theory
    • Dennis J.E. Jr., Morè J.J. Quasi-Newton methods, motivation and theory. SIAM Rev. 19:1977;46-89.
    • (1977) SIAM Rev. , vol.19 , pp. 46-89
    • Dennis J.E., Jr.1    Morè, J.J.2
  • 30
    • 84974231501 scopus 로고
    • Aspects of the numerical analysis of neural networks
    • Ellacott S.W. Aspects of the numerical analysis of neural networks. Acta Numer. 3:1994;145-202.
    • (1994) Acta Numer. , vol.3 , pp. 145-202
    • Ellacott, S.W.1
  • 31
    • 0003451149 scopus 로고
    • Nonlinear Programming : Sequential Unconstrained Minimization Techniques
    • Wiley, New York, SIAM Publications, Philadelphia, PA 19104-2688, USA
    • A.V. Fiacco, G.P. McCormick, Nonlinear Programming : Sequential Unconstrained Minimization Techniques, Wiley, New York, 1968 Reprint: Volume 4 of SIAM Classics in Applied Mathematics, SIAM Publications, Philadelphia, PA 19104-2688, USA, 1990).
    • (1968) Reprint: Volume 4 of SIAM Classics in Applied Mathematics
    • Fiacco, A.V.1    McCormick, G.P.2
  • 34
    • 0000615669 scopus 로고
    • Function minimization by conjugate gradients
    • Fletcher R., Reeves C.M. Function minimization by conjugate gradients. Comput. J. 7:1964;149-154.
    • (1964) Comput. J. , vol.7 , pp. 149-154
    • Fletcher, R.1    Reeves, C.M.2
  • 35
    • 0030531116 scopus 로고    scopus 로고
    • Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization
    • Forsgren A., Gill P.E., Shinnerl J.R. Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization. SIAM J. Matrix Anal. Appl. 17:1996;187-211.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 187-211
    • Forsgren, A.1    Gill, P.E.2    Shinnerl, J.R.3
  • 38
    • 0039169768 scopus 로고    scopus 로고
    • Large Scale Unconstrained Optimization
    • in: I.S. Duff, G.A. Watson (Eds.), Clarendon, Oxford, UK
    • J. Nocedal, Large Scale Unconstrained Optimization, in: I.S. Duff, G.A. Watson (Eds.), The State of the Art in Numerical Analysis, Clarendon, Oxford, UK, 1997, pp. 311-338.
    • (1997) The State of the Art in Numerical Analysis , pp. 311-338
    • Nocedal, J.1
  • 41
    • 0000924593 scopus 로고
    • Numerical methods for solving least squares problems
    • Golub G. Numerical methods for solving least squares problems. Numer. Math. 7:1965;206-216.
    • (1965) Numer. Math. , vol.7 , pp. 206-216
    • Golub, G.1
  • 43
    • 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
  • 44
    • 34250081478 scopus 로고
    • Fast orthogonal decomposition of rank deficient Toeplitz matrices
    • Hansen P.C., Gesmar H. Fast orthogonal decomposition of rank deficient Toeplitz matrices. Numer. Algorithms. 4:1993;151-166.
    • (1993) Numer. Algorithms , vol.4 , pp. 151-166
    • Hansen, P.C.1    Gesmar, H.2
  • 45
    • 0039762265 scopus 로고    scopus 로고
    • Harwell subroutine library, HSL Office, Culham, Oxon OX14 3ED, United Kingdom
    • Harwell subroutine library, HSL Office, Culham, Oxon OX14 3ED, United Kingdom, http: // www.cse.clrc.ac.uk / Activity / HSL.
  • 46
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Hestenes M.R., Stiefel E. Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Standards. 49:1952;409-436.
    • (1952) J. Res. Natl. Bur. Standards , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 47
    • 0001005483 scopus 로고
    • Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems
    • Higham N.J. Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Numer. Math. 50:1987;613-632.
    • (1987) Numer. Math. , vol.50 , pp. 613-632
    • Higham, N.J.1
  • 49
    • 0003157339 scopus 로고
    • Robust estimation of a location parameter
    • Huber P.J. Robust estimation of a location parameter. Ann. Math. Statist. 35:1964;73-101.
    • (1964) Ann. Math. Statist. , vol.35 , pp. 73-101
    • Huber, P.J.1
  • 51
    • 0000665794 scopus 로고
    • Displacement structure: Theory and applications
    • Kailath T., Sayed A.H. Displacement structure: theory and applications. SIAM Rev. 37:1995;297-386.
    • (1995) SIAM Rev. , vol.37 , pp. 297-386
    • Kailath, T.1    Sayed, A.H.2
  • 52
    • 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
  • 53
    • 34249921043 scopus 로고
    • Computational results of an interior point algorithm for large scale linear programming
    • Karmarkar N.K., Ramakrishnan K.G. Computational results of an interior point algorithm for large scale linear programming. Math. Programming. 52:1991;555-586.
    • (1991) Math. Programming , vol.52 , pp. 555-586
    • Karmarkar, N.K.1    Ramakrishnan, K.G.2
  • 54
    • 0016993685 scopus 로고
    • A constructive proof of the Brouwer fixed-point theorem and computational results
    • Kellogg R.B., Li T.-Y., 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
  • 55
    • 0000769618 scopus 로고
    • A polynomial algorithm in linear programming
    • Khachian L.G. A polynomial algorithm in linear programming. Dokl. Akad. Nauk SSSR. 244:1979;1093-1096.
    • (1979) Dokl. Akad. Nauk SSSR , vol.244 , pp. 1093-1096
    • Khachian, L.G.1
  • 56
    • 0001849163 scopus 로고
    • How good is the simplex algorithm?
    • In: O. Shisha, (Ed.), Academic Press, New York
    • V. Klee, G.J. Minty, How good is the simplex algorithm? In: O. Shisha, (Ed.), Inequalities III, Academic Press, New York, 1972, pp. 159-175.
    • (1972) Inequalities III , pp. 159-175
    • Klee, V.1    Minty, G.J.2
  • 57
    • 0032333546 scopus 로고    scopus 로고
    • BFGS with update skipping and varying memory
    • Kolda T., O'Leary D.P., Nazareth L. BFGS with update skipping and varying memory. SIAM J. Optim. 8:1998;1060-1083.
    • (1998) SIAM J. Optim. , vol.8 , pp. 1060-1083
    • Kolda, T.1    O'Leary, D.P.2    Nazareth, L.3
  • 59
    • 0003476369 scopus 로고
    • Prentice-Hall, Englewood Cliffs, NJ, 1974: reprinted by SIAM, Philadelphia, PA
    • C.L. Lawson, R.J. Hanson, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, NJ, 1974: reprinted by SIAM, Philadelphia, PA, 1995.
    • (1995) Solving Least Squares Problems
    • Lawson, C.L.1    Hanson, R.J.2
  • 60
  • 64
    • 0001662422 scopus 로고
    • Interior point methods for linear programming: Computational state of the art
    • Lustig I.J., Marsten R.E., Shanno D.F. Interior point methods for linear programming: computational state of the art. ORSA J. Comput. 6(1):1994;1-14.
    • (1994) ORSA J. Comput. , vol.6 , Issue.1 , pp. 1-14
    • Lustig, I.J.1    Marsten, R.E.2    Shanno, D.F.3
  • 65
    • 0026838079 scopus 로고
    • Implementation of affine scaling methods: Approximate solutions of systems of linear equations using preconditioned conjugate gradient methods
    • Mehrotra S. Implementation of affine scaling methods: Approximate solutions of systems of linear equations using preconditioned conjugate gradient methods. ORSA J. Comput. 4(2):1992;103-118.
    • (1992) ORSA J. Comput. , vol.4 , Issue.2 , pp. 103-118
    • Mehrotra, S.1
  • 67
    • 0040948345 scopus 로고
    • Ph.D. Thesis, North Carolina State University, Raleigh, NC
    • J.G. Nagy, Toeplitz least squares computations, Ph.D. Thesis, North Carolina State University, Raleigh, NC, 1991.
    • (1991) Toeplitz Least Squares Computations
    • Nagy, J.G.1
  • 68
    • 0039169761 scopus 로고
    • Optimization techniques in linear regression: A review
    • Narula S.C. Optimization techniques in linear regression: a review. TIMS. / Stud. Management Sci. 19:1982;11-29.
    • (1982) TIMS / Stud. Management Sci. , vol.19 , pp. 11-29
    • Narula, S.C.1
  • 69
    • 0001585735 scopus 로고
    • Preconditioning of truncated-Newton methods
    • Nash S.G. Preconditioning of truncated-Newton methods. SIAM J. Sci. Statist. Comput. 6:1985;599-616.
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 599-616
    • Nash, S.G.1
  • 70
    • 84966262179 scopus 로고
    • Updating quasi-Newton matrices with limited storage
    • Nocedal J. Updating quasi-Newton matrices with limited storage. Math. Comp. 35:1980;773-782.
    • (1980) Math. Comp. , vol.35 , pp. 773-782
    • Nocedal, J.1
  • 71
    • 84972047841 scopus 로고
    • Theory of algorithms for unconstrained optimization
    • Nocedal J. Theory of algorithms for unconstrained optimization. Acta Numerica. 1:1992;199-242.
    • (1992) Acta Numerica , vol.1 , pp. 199-242
    • Nocedal, J.1
  • 72
    • 0020129823 scopus 로고
    • A discrete Newton algorithm for minimizing a function of many variables
    • O'Leary D.P. A discrete Newton algorithm for minimizing a function of many variables. Math. Programming. 23:1982;20-33.
    • (1982) Math. Programming , vol.23 , pp. 20-33
    • O'Leary, D.P.1
  • 73
    • 0000115216 scopus 로고
    • Robust regression computation using iteratively reweighted least squares
    • O'Leary D.P. Robust regression computation using iteratively reweighted least squares. SIAM J. Matrix Anal. Appl. 11:1990;466-480.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 466-480
    • O'Leary, D.P.1
  • 75
    • 0013441963 scopus 로고    scopus 로고
    • Forward: Special issue on semidefinite programming
    • Overton M., Wolkowicz H. Forward: special issue on semidefinite programming. Math. Programming. 77:1997;105-110.
    • (1997) Math. Programming , vol.77 , pp. 105-110
    • Overton, M.1    Wolkowicz, H.2
  • 76
    • 0031509346 scopus 로고    scopus 로고
    • Stability analysis and fast algorithms for triangularization of Toeplitz matrices
    • Park H., Eldén L. Stability analysis and fast algorithms for triangularization of Toeplitz matrices. Numer. Math. 76:1997;383-402.
    • (1997) Numer. Math. , vol.76 , pp. 383-402
    • Park, H.1    Eldén, L.2
  • 77
    • 0014827294 scopus 로고
    • The least squares problem and pseudo-inverses
    • Peters G., Wilkinson J.H. The least squares problem and pseudo-inverses. Comput. J. 13:1970;309-316.
    • (1970) Comput. J. , vol.13 , pp. 309-316
    • Peters, G.1    Wilkinson, J.H.2
  • 79
    • 0034147823 scopus 로고    scopus 로고
    • A truncated primal-infeasible dual-feasible network interior point method
    • to appear
    • L.F. Portugal, M.G.C. Resende, G. Veiga, J.J. Júdice, A truncated primal-infeasible dual-feasible network interior point method, Networks ( 2000 ), to appear.
    • (2000) Networks
    • Portugal, L.F.1    Resende, M.G.C.2    Veiga, G.3    Júdice, J.J.4
  • 80
    • 0040948325 scopus 로고
    • A Note on the least squares solution of a band system of linear equations by Householder reductions
    • Reid J.K. A Note on the least squares solution of a band system of linear equations by Householder reductions. Comput J. 10:1967;188-189.
    • (1967) Comput J. , vol.10 , pp. 188-189
    • Reid, J.K.1
  • 81
    • 0039169750 scopus 로고    scopus 로고
    • Cholesky-based methods for sparse least squares: The benefits of regularization
    • L. Adams, & J.L. Nazareth. Philadelphia, PA: SIAM
    • Saunders M.A. Cholesky-based methods for sparse least squares: the benefits of regularization. Adams L., Nazareth J.L. Linear and Nonlinear Conjugate Gradient-Related Methods. 1996;92-100 SIAM, Philadelphia, PA.
    • (1996) Linear and Nonlinear Conjugate Gradient-Related Methods , pp. 92-100
    • Saunders, M.A.1
  • 83
    • 0005223906 scopus 로고    scopus 로고
    • Interior point methods for linear and nonlinear programming
    • I.S. Duff, & G.A. Watson. Oxford, England: Clarendon Press
    • Shanno D.F., Simantiraki E.M. Interior point methods for linear and nonlinear programming. Duff I.S., Watson G.A. The State of the Art in Numerical Analysis. 1997;339-362 Clarendon Press, Oxford, England.
    • (1997) The State of the Art in Numerical Analysis , pp. 339-362
    • Shanno, D.F.1    Simantiraki, E.M.2
  • 84
    • 84966259276 scopus 로고
    • Modifying pivot elements in Gaussian elimination
    • Stewart G.W. Modifying pivot elements in Gaussian elimination. Math. Comp. 28(126):1974;537-542.
    • (1974) Math. Comp. , vol.28 , Issue.126 , pp. 537-542
    • Stewart, G.W.1
  • 85
    • 0027879547 scopus 로고
    • On the early history of the singular value decomposition
    • Stewart G.W. On the early history of the singular value decomposition. SIAM Rev. 35:1993;551-566.
    • (1993) SIAM Rev. , vol.35 , pp. 551-566
    • Stewart, G.W.1
  • 86
    • 0003050332 scopus 로고
    • Fast Toeplitz orthogonalization
    • Sweet D.R. Fast Toeplitz orthogonalization. Numer. Math. 43:1984;1-21.
    • (1984) Numer. Math. , vol.43 , pp. 1-21
    • Sweet, D.R.1
  • 89
    • 0010864753 scopus 로고
    • Pattern recognition using generalized portraits
    • V. Vapnik, A.Ya. Lerner, Pattern recognition using generalized portraits, Automat. Remote Control 24 (1963) 709-719; transl. from Avtomatika i Telemekhanika 24 (6) (1963) 774-780.
    • (1963) Automat. Remote Control , vol.24 , pp. 709-719
    • Vapnik, V.1    Lerner, A.Ya.2
  • 90
    • 0010864753 scopus 로고
    • transl. from
    • V. Vapnik, A.Ya. Lerner, Pattern recognition using generalized portraits, Automat. Remote Control 24 (1963) 709-719; transl. from Avtomatika i Telemekhanika 24 (6) (1963) 774-780.
    • (1963) Avtomatika I Telemekhanika , vol.24 , Issue.6 , pp. 774-780
  • 92
    • 0039762248 scopus 로고    scopus 로고
    • Adaptive use of iterative methods in predictor-corrector interior point methods for linear programming
    • Technical Report CS-TR-4011, Computer Science Department, University of Maryland, College Park, MD, April to appear
    • W. Wang, D.P. O'Leary, Adaptive use of iterative methods in predictor-corrector interior point methods for linear programming, Technical Report CS-TR-4011, Computer Science Department, University of Maryland, College Park, MD, April 1999, Numer. Algorithms, to appear.
    • (1999) Numer. Algorithms
    • Wang, W.1    O'Leary, D.P.2
  • 94
    • 0031345669 scopus 로고    scopus 로고
    • Algorithm 777: HOMPACK90: A suite of Fortran 90 codes for globally convergent homotopy algorithms
    • Watson L.T., Sosonkina M., Melville R.C., Morgan A.P., Walker H.F. Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms. ACM Trans. Math. Software. 23:1997;514-549.
    • (1997) ACM Trans. Math. Software , vol.23 , pp. 514-549
    • Watson, L.T.1    Sosonkina, M.2    Melville, R.C.3    Morgan, A.P.4    Walker, H.F.5
  • 95
    • 0000195992 scopus 로고
    • Perturbation theory for pseudo-inverses
    • Wedin P.-Å. Perturbation theory for pseudo-inverses. BIT. 13:1973;217-232.
    • (1973) BIT , vol.13 , pp. 217-232
    • Wedin, P.-Å.1
  • 96
    • 84971922797 scopus 로고
    • Interior methods for constrained optimization
    • Wright M.H. Interior methods for constrained optimization. Acta Numerica. 1:1992;341-407.
    • (1992) Acta Numerica , vol.1 , pp. 341-407
    • Wright, M.H.1
  • 97
    • 0029535607 scopus 로고
    • Historical development of the Newton-Raphson method
    • Ypma T.J. Historical development of the Newton-Raphson method. SIAM Rev. 37:1995;531-551.
    • (1995) SIAM Rev. , vol.37 , pp. 531-551
    • Ypma, T.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.