메뉴 건너뛰기




Volumn 66, Issue 220, 1997, Pages 1461-1486

Numerical solution of isospectral flows

Author keywords

Conservation laws; Isospectral flows; Runge Kutta methods; Toda lattice equations; Unitary flows

Indexed keywords


EID: 0031488281     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00902-2     Document Type: Article
Times cited : (89)

References (32)
  • 1
    • 0002412868 scopus 로고
    • Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
    • MR 92j:90043
    • R. W. Brockett "Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems", Lin. Alg. Appl., 146 (1991), 79-91. MR 92j:90043
    • (1991) Lin. Alg. Appl. , vol.146 , pp. 79-91
    • Brockett, R.W.1
  • 2
    • 84968517727 scopus 로고
    • A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map
    • MR 91e:58067
    • A. M. Bloch, R. W. Brockett and T. Ratiu, "A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map", Bull. Amer. Math. Soc., 23 (1990), 477-485. MR 91e:58067
    • (1990) Bull. Amer. Math. Soc. , vol.23 , pp. 477-485
    • Bloch, A.M.1    Brockett, R.W.2    Ratiu, T.3
  • 3
    • 0004165067 scopus 로고
    • Gordon and Breach Science Publishers, New York, London, Paris, MR 58:1979
    • T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach Science Publishers, New York, London, Paris, 1978. MR 58:1979
    • (1978) An Introduction to Orthogonal Polynomials
    • Chihara, T.S.1
  • 4
    • 0040830341 scopus 로고
    • The generalized Toda flow, the QR algorithm and the center manifold theory
    • MR 86g:58071
    • M. T. Chu, "The generalized Toda flow, the QR algorithm and the center manifold theory", SIAM J. Alg. Discr. Math., 5 (1984), 187-201. MR 86g:58071
    • (1984) SIAM J. Alg. Discr. Math. , vol.5 , pp. 187-201
    • Chu, M.T.1
  • 5
    • 0025474861 scopus 로고
    • The projected gradient method for least squares matrix approximations with spectral constraints
    • MR 91f:65073
    • M. T. Chu and K. R. Driessel, "The projected gradient method for least squares matrix approximations with spectral constraints", SIAM J. Numer Anal., 27 (1990), 1050-1060. MR 91f:65073
    • (1990) SIAM J. Numer Anal. , vol.27 , pp. 1050-1060
    • Chu, M.T.1    Driessel, K.R.2
  • 7
    • 0002211850 scopus 로고
    • Stability of Runge-Kutta methods for trajectory problems
    • MR 90d:65133
    • G. J. Cooper, "Stability of Runge-Kutta methods for trajectory problems", IMA J. Numer. Anal., 7 (1987), 1-13. MR 90d:65133
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 1-13
    • Cooper, G.J.1
  • 8
    • 0040830340 scopus 로고
    • On isospectral gradient flows solving matrix eigenproblems using differential equations
    • J. R. Cannon and U. Hournung eds., Birkhauser-Verlag . MR 88h:58097
    • K. R. Driessel, "On isospectral gradient flows solving matrix eigenproblems using differential equations", Inverse Problems, J. R. Cannon and U. Hournung eds., Birkhauser-Verlag (1986), 69-90. MR 88h:58097
    • (1986) Inverse Problems , pp. 69-90
    • Driessel, K.R.1
  • 9
    • 0002553195 scopus 로고
    • Ordinary differential equations and the symmetric eigenvalue problem
    • MR 86k:58101
    • P. Deift, T. Nanda and C. Tomei, "Ordinary differential equations and the symmetric eigenvalue problem", SIAM J. Numer. Anal., 20 (1983), 1-22. MR 86k:58101
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 1-22
    • Deift, P.1    Nanda, T.2    Tomei, C.3
  • 11
    • 0028374128 scopus 로고
    • Unitary integrators and applications to continuous orthonormalization techniques
    • MR 95a:65121
    • L. Dieci, R. D. Russell and E. S. van Vleck, "Unitary integrators and applications to continuous orthonormalization techniques", SIAM J. Numer. Anal., 31 (1994), 261-281. MR 95a:65121
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 261-281
    • Dieci, L.1    Russell, R.D.2    Van Vleck, E.S.3
  • 12
    • 0001580611 scopus 로고
    • Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods
    • MR 92m:65090
    • T. Eirola and J. M. Sanz-Serna, "Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods", Numer. Math., 61 (1992), 281-290. MR 92m:65090
    • (1992) Numer. Math. , vol.61 , pp. 281-290
    • Eirola, T.1    Sanz-Serna, J.M.2
  • 13
    • 25344451956 scopus 로고
    • The Toda lattice
    • MR 53:12411
    • H. Flaschka, "The Toda lattice", I. Phys. Rev. B9 (1974), 1924-25. MR 53:12411
    • (1974) I. Phys. Rev. , vol.B9 , pp. 1924-1925
    • Flaschka, H.1
  • 16
    • 0039051778 scopus 로고
    • Singular value decomposition via gradient flows
    • U. Helmke and J. B. Moore, "Singular value decomposition via gradient flows", Systems Control Lett., 14 (1990), 369-377.
    • (1990) Systems Control Lett. , vol.14 , pp. 369-377
    • Helmke, U.1    Moore, J.B.2
  • 18
    • 0001351202 scopus 로고
    • Solving linear ordinary differential equations by exponentials of iterated commutators
    • MR 86b:65074
    • A. Iserles, "Solving linear ordinary differential equations by exponentials of iterated commutators", Numer. Math., 45 (1984), 183-199. MR 86b:65074
    • (1984) Numer. Math. , vol.45 , pp. 183-199
    • Iserles, A.1
  • 19
    • 0000955168 scopus 로고
    • On explicitly solvable systems of differential equations related to certain Toda lattices
    • MR 51:6182
    • M. Kac and P. van Moerbeke, "On explicitly solvable systems of differential equations related to certain Toda lattices", Adv. in Math., 16 (1975), 160-169. MR 51:6182
    • (1975) Adv. in Math. , vol.16 , pp. 160-169
    • Kac, M.1    Van Moerbeke, P.2
  • 20
    • 0040830338 scopus 로고
    • Monotonicity properties of the Toda flow, the QR-flow and subspace iteration
    • MR 93f:15014
    • J. Lagarias, "Monotonicity properties of the Toda flow, the QR-flow and subspace iteration", SIAM J. Matrix Anal. Appl., 12, 3 (1991), 449-462. MR 93f:15014
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , Issue.3 , pp. 449-462
    • Lagarias, J.1
  • 22
    • 21344491116 scopus 로고
    • Numerical gradient algorithms for eigenvalue and singular value calculations
    • MR 95f:65079
    • J. B. Moore, R. E. Mahony and U. Helmke, "Numerical gradient algorithms for eigenvalue and singular value calculations", SIAM J. Matrix Anal. Appl., 15 (1994), 881-902. MR 95f:65079
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 881-902
    • Moore, J.B.1    Mahony, R.E.2    Helmke, U.3
  • 23
    • 0000641586 scopus 로고
    • Finitely many mass points on the line under the influence of an exponential potential - An integrable system
    • (J. Moser, ed.) Springer-Verlag, New York, Berlin, Heildelberg, MR 56:13279
    • J. Moser, "Finitely many mass points on the line under the influence of an exponential potential - An integrable system", Dynamic Systems Theory and Applications, (J. Moser, ed.) Springer-Verlag, New York, Berlin, Heildelberg, 1975, 467-497. MR 56:13279
    • (1975) Dynamic Systems Theory and Applications , pp. 467-497
    • Moser, J.1
  • 24
    • 0040235752 scopus 로고
    • Ph.D. Thesis, New York Univ., New York
    • T. Nanda, Ph.D. Thesis, New York Univ., New York, 1982.
    • (1982)
    • Nanda, T.1
  • 25
    • 0022050195 scopus 로고
    • Differential equations and the QR algorithm
    • MR 87h:34012
    • T. Nanda, "Differential equations and the QR algorithm", SIAM J. Numer. Anal., 22 (1985), 310-321. MR 87h:34012
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 310-321
    • Nanda, T.1
  • 26
    • 0003805793 scopus 로고
    • Springer-Verlag, Berlin, Heildelberg, New York . MR 82k:58052b
    • M. Toda, Theory of Nonlinear Lattices, Springer-Verlag, Berlin, Heildelberg, New York (1981). MR 82k:58052b
    • (1981) Theory of Nonlinear Lattices
    • Toda, M.1
  • 27
    • 0000434148 scopus 로고
    • The QR algorithm and scattering for the finite nonperiodic Toda lattice
    • MR 83h:58053
    • W. W. Symes, "The QR algorithm and scattering for the finite nonperiodic Toda lattice", Phys. D., 4 (1982), 275-280. MR 83h:58053
    • (1982) Phys. D. , vol.4 , pp. 275-280
    • Symes, W.W.1
  • 28
    • 0038976122 scopus 로고
    • Runge-Kutta schemes for Hamiltonian systems
    • MR 90b:65145
    • J. M. Sanz-Serna, "Runge-Kutta schemes for Hamiltonian systems", BIT, 28 (1988), 877-883. MR 90b:65145
    • (1988) BIT , vol.28 , pp. 877-883
    • Sanz-Serna, J.M.1
  • 30
    • 77957214313 scopus 로고
    • Conservative and nonconservative schemes for the solution of the nonlineal Schrödinger equation
    • MR 89h:65153
    • J. M. Sanz-Serna and J. G. Verwer, "Conservative and nonconservative schemes for the solution of the nonlineal Schrödinger equation", IMA J. Numer. Anal., 6 (1986), 25-42. MR 89h:65153
    • (1986) IMA J. Numer. Anal. , vol.6 , pp. 25-42
    • Sanz-Serna, J.M.1    Verwer, J.G.2
  • 31
    • 0021452861 scopus 로고
    • Isospectral flows
    • MR 86d:58054
    • D. S. Watkins, "Isospectral flows", SIAM Rev., 26 (1984), 379-391. MR 86d:58054
    • (1984) SIAM Rev. , vol.26 , pp. 379-391
    • Watkins, D.S.1
  • 32
    • 0039051780 scopus 로고
    • Self-equivalent flows associated with the singular value decomposition
    • MR 90m:65064
    • D. Watkins and L. Elsner, "Self-equivalent flows associated with the singular value decomposition", SIAM J. Matrix Anal. Appl., 10 (1989), 244-258. MR 90m:65064
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 244-258
    • Watkins, D.1    Elsner, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.