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A new nonlinear dynamical system that leads to eigenvalues

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An Erratum to this article was published on 01 June 1992

Abstract

This paper presents a new dynamical system of Lax type which solves the skew-Hermitian eigenvalue problem. The solution of the system is found to converge to a diagonal matrix which is a permutation of the eigenvalues of the initial value matrix.

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References

  1. V.I. Arnol’d and A.B. Givental’, Symplectic geometry. Dynamical Systems IV (eds. V.I. Arnol’d and S.P. Novikov), Encyc. Math. Sci. Vol. 4, Springer-Verlag, Berlin, 1990, 1–136.

    Google Scholar 

  2. A.M. Bloch, A completely integrable Hamiltonian system associated with line fitting in complex vector space. Bull. Amer. Math. Soc. (New Series),12 (1985), 250–254.

    Article  MATH  MathSciNet  Google Scholar 

  3. 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 moment map. Bull Amer. Math. Soc. (New Series),23 (1990), 477–485.

    Article  MATH  MathSciNet  Google Scholar 

  4. R.W. Brockett, Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems. Proc. 27th IEEE Conf. on Decision and Control, IEEE, 1988, 799–803.

  5. W.W. Chu, The generalized Toda flow, theQR algorithm and the center manifold theory. SIAM J. Algebraic Discrete Methods,5 (1984), 187–201.

    Article  MATH  MathSciNet  Google Scholar 

  6. W.W. Chu, On the continuous realization of iterative processes. SIAM Rev.,30 (1988), 375–387.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Deift, T. Nanda and C. Tomei, Ordinary differential equations and the symmetric eigenvalue problem. SIAM J. Numer. Anal.,20 (1983), 1–22.

    Article  MATH  MathSciNet  Google Scholar 

  8. V. Guillemin and S. Sternberg, Convexity properties of the moment mapping., Invent. Math.,67 (1982), 491–513.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Moser, Finitely many points on the line under the influence of an exponential potential — An integrable system. Dynamical Systems, Theory and Applications (ed. J. Moser), Lecture Notes in Phys. Vol. 38, Springer-Verlag, Berlin, 1975, 467–497.

    Chapter  Google Scholar 

  10. Y. Nakamura, Lax equations associated with a least squares problem and compact Lie algebras. To be published in Adv. Stud. Pure Math. Vol. 22.

  11. Y. Nakamura, The level manifold of a generalized Toda equation hierarchy. To be published in Trans. Amer. Math. Soc.

  12. W.W. Symes, TheQR algorithm and scattering for the finite nonperiodic Toda lattice. Physica,4D (1982), 275–280.

    MathSciNet  Google Scholar 

  13. D.S. Watkins, Isospectral flows. SIAM Rev.,26 (1984), 379–392.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Gifu University, Yanagido, 501-11, Gifu, Japan

    Yoshimasa Nakamura

Authors
  1. Yoshimasa Nakamura
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Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/BF03167570.

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Nakamura, Y. A new nonlinear dynamical system that leads to eigenvalues. Japan J. Indust. Appl. Math. 9, 133–139 (1992). https://doi.org/10.1007/BF03167198

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  • DOI: https://doi.org/10.1007/BF03167198

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