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The Rational Krylov Algorithm for Nonlinear Matrix Eigenvalue Problems

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Abstract

It is shown how the rational Krylov algorithm can be applied to a matrix eigenvalue problem that is nonlinear in the eigenvalue parameter. Bibliography: 6 titles.

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REFERENCES

  1. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, eds., Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, SIAM, Philadelphia (2000).

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  2. P. Hager and N.-E. Wiberg, “The rational Krylov algorithm for nonlinear eigenvalue problems," submitted (2000).

  3. V. N. Kublanovskaya, “On an application of Newton's method to the determination of eigenvalues of ?-matrices," Dokl. Akad. Nauk SSSR, 10, 1240–1241 (1969).

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  4. V. N. Kublanovskaya, “On an approach to the solution of the generalized latent value problem for ?-matrices," SIAM J. Numer. Anal., 7, 532–537 (1970).

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  5. A. Ruhe, “Algorithms for the nonlinear algebraic eigenvalue problem," SIAM J. Numer. Anal., 10, 674–689 (1973).

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  1. Department of Mathematics, Chalmers Institute of Technology and the, University of Göteborg, S-41296, Göteborg, Sweden

    A. Ruhe

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  1. A. Ruhe
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Ruhe, A. The Rational Krylov Algorithm for Nonlinear Matrix Eigenvalue Problems. Journal of Mathematical Sciences 114, 1854–1856 (2003). https://doi.org/10.1023/A:1022414805217

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