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Mathematics of Computation

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Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem

Author: Zhaojun Bai
Journal: Math. Comp. 62 (1994), 209-226
MSC: Primary 65F15
MathSciNet review: 1201066
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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.

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Keywords: Nonsymmetric matrices, eigenvalue problem, error analysis, Lanczos method
Article copyright: © Copyright 1994 American Mathematical Society