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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem
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by Zhaojun Bai PDF
Math. Comp. 62 (1994), 209-226 Request permission

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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 62 (1994), 209-226
  • MSC: Primary 65F15
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1201066-7
  • MathSciNet review: 1201066