The Rational Krylov Algorithm for Nonlinear Matrix Eigenvalue Problems
- 69 Downloads
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.
Unable to display preview. Download preview PDF.
- 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.P. Hager and N.-E. Wiberg, “The rational Krylov algorithm for nonlinear eigenvalue problems," submitted (2000).Google Scholar
- 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.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.A. Ruhe, “Algorithms for the nonlinear algebraic eigenvalue problem," SIAM J. Numer. Anal., 10, 674–689 (1973).Google Scholar
- 6.A. Ruhe, “Rational Krylov, a practical algorithm for large sparse nonsymmetric matrix pencils," SIAM J. Sci. Comp., 19, 1535–1551 (1998).Google Scholar
© Plenum Publishing Corporation 2003