## Error Analysis of the Lanczos Algorithm for the Nonsymmetric Eigenvalue Problem (1994)

Venue: | Math. Comp |

Citations: | 19 - 3 self |

### BibTeX

@ARTICLE{Bai94erroranalysis,

author = {Zhaojun Bai},

title = {Error Analysis of the Lanczos Algorithm for the Nonsymmetric Eigenvalue Problem},

journal = {Math. Comp},

year = {1994},

volume = {62},

pages = {209--226}

}

### OpenURL

### 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 analogy 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 in this paper. 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 Ritz triplet in terms of small residuals. Numerical experimental results demonstrate such observation. Key words: nonsymmetric matrices, eigenvalue problem, error analysis, Lanczos method. AMS(MOS) Classification: 65F15, 65F10 1 Introduction This paper is concerned with an error analysis of the Lanczos algorithm for solving the nonsymmetric eigenvalue problem of a given real n 2 n matrix A: Ax = x; y H...