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Volumn 34, Issue 3, 1997, Pages 867-880

Computation of Singularities in Large Nonlinear Systems

Author keywords

Bordered matrix; Lyapunov Schmidt reduction

Indexed keywords


EID: 0009576092     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994272167     Document Type: Article
Times cited : (14)

References (30)
  • 1
    • 0039231630 scopus 로고
    • Defining equations for singular solutions and numerical applications
    • T. Küpper, H. Mittelmann, and H. Weber, eds., Birkhäuser-Verlag, Basel, Switzerland
    • W.-J. BEYN, Defining equations for singular solutions and numerical applications, in Numerical Methods for Bifurcation Problems, International Series of Numerical Mathematics 70, T. Küpper, H. Mittelmann, and H. Weber, eds., Birkhäuser-Verlag, Basel, Switzerland, 1984, pp. 42-56.
    • (1984) Numerical Methods for Bifurcation Problems, International Series of Numerical Mathematics , vol.70 , pp. 42-56
    • Beyn, W.-J.1
  • 2
    • 0024776756 scopus 로고
    • Regularization and computation of a bifurcation with corank 2
    • K. BÖHMER AND MEI ZHEN, Regularization and computation of a bifurcation with corank 2, Computing, 41 (1989), pp. 307-316.
    • (1989) Computing , vol.41 , pp. 307-316
    • Böhmer, K.1    Zhen, M.2
  • 3
    • 0039050372 scopus 로고
    • Techniques for large sparse systems arising from continuation methods
    • T. Küpper, H. Mittelmann, and H. Weber, eds., Birkhäuser-Verlag, Basel, Switzerland
    • T. F. CHAN, Techniques for large sparse systems arising from continuation methods, in Numerical Methods for Bifurcation Problems, International Series of Numerical Mathematics 70, T. Küpper, H. Mittelmann, and H. Weber, eds., Birkhäuser-Verlag, Basel, Switzerland, 1984, pp. 116-128.
    • (1984) Numerical Methods for Bifurcation Problems, International Series of Numerical Mathematics , vol.70 , pp. 116-128
    • Chan, T.F.1
  • 4
    • 0000873548 scopus 로고
    • Newton-like pseudo-arclength methods for computing simple turning points
    • T. F. CHAN, Newton-like pseudo-arclength methods for computing simple turning points, SIAM J. Sci. Statist. Comput., 5 (1984), pp. 135-148.
    • (1984) SIAM J. Sci. Statist. Comput. , vol.5 , pp. 135-148
    • Chan, T.F.1
  • 5
    • 0000422884 scopus 로고
    • Multiple limit point bifurcation
    • D. W. DECKER AND H. B. KELLER, Multiple limit point bifurcation, J. Math. Anal. Appl., 75 (1980), pp. 417-430.
    • (1980) J. Math. Anal. Appl. , vol.75 , pp. 417-430
    • Decker, D.W.1    Keller, H.B.2
  • 9
    • 0042470959 scopus 로고
    • Mixed block elimination for linear systems with wider borders
    • W. GOVAERTS AND J. D. PRYCE, Mixed block elimination for linear systems with wider borders, IMA J. Numer. Anal., 13 (1993), pp. 161-180.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 161-180
    • Govaerts, W.1    Pryce, J.D.2
  • 10
    • 21844484668 scopus 로고
    • Bordered matrices and singularities of large nonlinear systems
    • W. GOVAERTS, Bordered matrices and singularities of large nonlinear systems, Internat. J. Bifurcation and Chaos, 5 (1995), pp. 243-250.
    • (1995) Internat. J. Bifurcation and Chaos , vol.5 , pp. 243-250
    • Govaerts, W.1
  • 11
    • 0021382437 scopus 로고
    • Characterization and computation of generalized turning points
    • A. GRIEWANK AND G. W. REDDIEN, Characterization and computation of generalized turning points, SIAM J. Numer. Anal., 21 (1984), pp. 176-185.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 176-185
    • Griewank, A.1    Reddien, G.W.2
  • 12
    • 38249023149 scopus 로고
    • Computation of cusp singularities for operator equations and their discretizations
    • A. GRIEWANK AND G. W. REDDIEN, Computation of cusp singularities for operator equations and their discretizations, J. Comput. Appl. Math., 26 (1989), pp. 133-153.
    • (1989) J. Comput. Appl. Math. , vol.26 , pp. 133-153
    • Griewank, A.1    Reddien, G.W.2
  • 13
    • 0000157103 scopus 로고
    • New algorithms for the evaluation of complex bifurcation points in ordinary differential equations. A comparative study
    • M. HOLODNIOK AND M. KUBIČEK, New algorithms for the evaluation of complex bifurcation points in ordinary differential equations. A comparative study, Appl. Math. Comput., 15 (1984), pp. 261-274.
    • (1984) Appl. Math. Comput. , vol.15 , pp. 261-274
    • Holodniok, M.1    Kubiček, M.2
  • 14
    • 0041049707 scopus 로고
    • Numerical applications of equivariant reduction techniques
    • E. Allgower, K. Böhmer, and M. Golubitsky, eds., Birkhaüser-Verlag, Basel, Switzerland
    • V. JANOVSKÝ AND P. PLECHÁČ, Numerical applications of equivariant reduction techniques, in Bifurcation and Symmetry, International Series of Numerical Mathematics 104, E. Allgower, K. Böhmer, and M. Golubitsky, eds., Birkhaüser-Verlag, Basel, Switzerland, 1992, pp. 203-213.
    • (1992) Bifurcation and Symmetry, International Series of Numerical Mathematics , vol.104 , pp. 203-213
    • Janovský, V.1    Plecháč, P.2
  • 15
    • 0039641417 scopus 로고
    • Singular points and their computation
    • T. Küpper, H. Mittelmann, and H. Weber, eds., Birkhäuser-Verlag, Basel, Switzerland
    • A. JEPSON AND A. SPENCE, Singular points and their computation, in Numerical Methods for Bifurcation Problems, T. Küpper, H. Mittelmann, and H. Weber, eds., Birkhäuser-Verlag, Basel, Switzerland, 1984, pp. 195-209.
    • (1984) Numerical Methods for Bifurcation Problems , pp. 195-209
    • Jepson, A.1    Spence, A.2
  • 16
    • 0022107708 scopus 로고
    • The numerical solution of nonlinear equations having several parameters I: Scalar equations
    • A. JEPSON AND A. SPENCE, The numerical solution of nonlinear equations having several parameters I: Scalar equations, SIAM J. Numer. Anal., 22 (1985), pp. 736-759.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 736-759
    • Jepson, A.1    Spence, A.2
  • 17
    • 0022052508 scopus 로고
    • Folds in solutions of two-parameter systems and their calculation. Part I
    • A. JEPSON AND A. SPENCE, Folds in solutions of two-parameter systems and their calculation. Part I., SIAM J. Numer. Anal., 22 (1985), pp. 347-368.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 347-368
    • Jepson, A.1    Spence, A.2
  • 18
    • 0002464199 scopus 로고
    • On a reduction process for nonlinear equations
    • A. JEPSON AND A. SPENCE, On a reduction process for nonlinear equations, SIAM J. Math. Anal., 20 (1989), pp. 39-56.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 39-56
    • Jepson, A.1    Spence, A.2
  • 20
    • 0346730339 scopus 로고
    • Constructive methods for bifurcation and nonlinear eigenvalue problems
    • K. Glowinsky and J. L. Lions, eds., Springer-Verlag, Berlin
    • H. B. KELLER, Constructive methods for bifurcation and nonlinear eigenvalue problems, in Computing Methods in Applied Sciences and Engineering, K. Glowinsky and J. L. Lions, eds., Springer-Verlag, Berlin, 1977, pp. 350-384.
    • (1977) Computing Methods in Applied Sciences and Engineering , pp. 350-384
    • Keller, H.B.1
  • 21
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and nonlinear eigenvalue problems
    • P. Rabinowitz, ed., Academic Press, New York
    • H. B. KELLER, Numerical solution of bifurcation and nonlinear eigenvalue problems, in Applications of Bifurcation Theory, P. Rabinowitz, ed., Academic Press, New York, 1977, pp. 359-384.
    • (1977) Applications of Bifurcation Theory , pp. 359-384
    • Keller, H.B.1
  • 22
    • 0001151327 scopus 로고
    • The bordering algorithm and path following near singular points of higher nullity
    • H. B. KELLER, The bordering algorithm and path following near singular points of higher nullity, SIAM J. Sci. Statist. Comput., 4 (1983), pp. 573-582.
    • (1983) SIAM J. Sci. Statist. Comput. , vol.4 , pp. 573-582
    • Keller, H.B.1
  • 23
    • 0000863468 scopus 로고
    • The calculation of turning points of nonlinear equations
    • G. MOORE AND A. SPENCE, The calculation of turning points of nonlinear equations, SIAM J. Numer. Anal., 17 (1980), pp. 567-576.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 567-576
    • Moore, G.1    Spence, A.2
  • 25
    • 0009644861 scopus 로고
    • Numerical determination of an emanating branch of Hopf bifurcation points in a two-parameter problem
    • D. ROOSE AND B. DE DIER, Numerical determination of an emanating branch of Hopf bifurcation points in a two-parameter problem, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 671-685.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 671-685
    • Roose, D.1    De Dier, B.2
  • 26
    • 0039823604 scopus 로고
    • Numerical computation of nonsimple turning points and cusps
    • D. ROOSE AND R. PIESSENS, Numerical computation of nonsimple turning points and cusps, Numer. Math., 46 (1985), pp. 189-211.
    • (1985) Numer. Math. , vol.46 , pp. 189-211
    • Roose, D.1    Piessens, R.2
  • 27
    • 0001475133 scopus 로고
    • Non-simple turning points and cusps
    • A. SPENCE AND B. WERNER, Non-simple turning points and cusps, IMA J. Numer. Anal., 2 (1982), pp. 413-427.
    • (1982) IMA J. Numer. Anal. , vol.2 , pp. 413-427
    • Spence, A.1    Werner, B.2
  • 28
    • 0010717668 scopus 로고
    • Test functions for bifurcation points and Hopf points in problems with symmetries
    • E. Allgower, K. Böhmer, and M. Golubitsky, eds., Birkhaüser-Verlag, Basel, Switzerland
    • B. WERNER, Test functions for bifurcation points and Hopf points in problems with symmetries, in Bifurcation and Symmetry, International Series of Numerical Mathematics 104, E. Allgower, K. Böhmer, and M. Golubitsky, eds., Birkhaüser-Verlag, Basel, Switzerland, 1992, pp. 317-327.
    • (1992) Bifurcation and Symmetry, International Series of Numerical Mathematics , vol.104 , pp. 317-327
    • Werner, B.1
  • 29
    • 0021418315 scopus 로고
    • The computation of symmetry-breaking bifurcation points
    • B. WERNER AND A. SPENCE, The computation of symmetry-breaking bifurcation points, SIAM J. Numer. Anal., 21 (1984), pp. 388-399.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 388-399
    • Werner, B.1    Spence, A.2
  • 30
    • 0024620677 scopus 로고
    • A numerical approximation for the simple bifurcation problems
    • MEI ZHEN, A numerical approximation for the simple bifurcation problems, Numer. Funct. Anal. Optim., 10 (1989), pp. 383-400.
    • (1989) Numer. Funct. Anal. Optim. , vol.10 , pp. 383-400
    • Zhen, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.