Journal of Mathematical Sciences

, Volume 114, Issue 6, pp 1854–1856 | Cite as

The Rational Krylov Algorithm for Nonlinear Matrix Eigenvalue Problems



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.


Eigenvalue Problem Matrix Eigenvalue Nonlinear Matrix Matrix Eigenvalue Problem Eigenvalue Parameter 
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  1. 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).Google Scholar
  2. 2.
    P. Hager and N.-E. Wiberg, “The rational Krylov algorithm for nonlinear eigenvalue problems," submitted (2000).Google Scholar
  3. 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).Google Scholar
  4. 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).Google Scholar
  5. 5.
    A. Ruhe, “Algorithms for the nonlinear algebraic eigenvalue problem," SIAM J. Numer. Anal., 10, 674–689 (1973).Google Scholar
  6. 6.
    A. Ruhe, “Rational Krylov, a practical algorithm for large sparse nonsymmetric matrix pencils," SIAM J. Sci. Comp., 19, 1535–1551 (1998).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. Ruhe
    • 1
  1. 1.Department of Mathematics, Chalmers Institute of Technology and theUniversity of GöteborgGöteborgSweden

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