Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem

Author:

Bai Zhaojun

Abstract

This paper presents an error analysis of the Lanczos algorithm in finite-precision arithmetic for solving the standard nonsymmetric eigenvalue problem, if no breakdown occurs. An analog of Paige’s theory on the relationship between the loss of orthogonality among the Lanczos vectors and the convergence of Ritz values in the symmetric Lanczos algorithm is discussed. The theory developed illustrates that in the nonsymmetric Lanczos scheme, if Ritz values are well conditioned, then the loss of biorthogonality among the computed Lanczos vectors implies the convergence of a group of Ritz triplets in terms of small residuals. Numerical experimental results confirm this observation.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference38 articles.

1. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. Mckenney, S. Ostrouchov, and D. Sorensen, LAPACK user’s guide, SIAM, Philadelphia, PA, 1992.

2. Z. Bai, A collection of test matrices for the large sparse nonsymmetric eigenvalue problem, University of Kentucky, Department of Mathematics, RR-93-03. Aug. 1993.

3. Nonsymmetric Lanczos and finding orthogonal polynomials associated with indefinite weights;Boley, Daniel L.;Numer. Algorithms,1991

4. Classics in Applied Mathematics;Cullum, Jane K.,2002

5. A practical procedure for computing eigenvalues of large sparse nonsymmetric matrices;Cullum, Jane,1986

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