A convergencea nalysis for nonsymmetric lanczos algorithms

Qiang Ye

doi:10.1090/S0025-5718-1991-1068826-4

A convergencea nalysis for nonsymmetric lanczos algorithms

Qiang Ye

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A convergence analysis for the nonsymmetric Lanczos algorithm is presented. By using a tridiagonal structure of the algorithm, some identities concerning Ritz values and Ritz vectors are established and used to derive approximation bounds. In particular, the analysis implies the classical results for the symmetric Lanczos algorithm.

Original language	English
Pages (from-to)	677-691
Number of pages	15
Journal	Mathematics of Computation
Volume	56
Issue number	194
DOIs	https://doi.org/10.1090/S0025-5718-1991-1068826-4
State	Published - Apr 1991

Keywords

Convergence bound
Lanczos algorithm
Tridiagonal matrices

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-1991-1068826-4

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title = "A convergencea nalysis for nonsymmetric lanczos algorithms",

abstract = "A convergence analysis for the nonsymmetric Lanczos algorithm is presented. By using a tridiagonal structure of the algorithm, some identities concerning Ritz values and Ritz vectors are established and used to derive approximation bounds. In particular, the analysis implies the classical results for the symmetric Lanczos algorithm.",

keywords = "Convergence bound, Lanczos algorithm, Tridiagonal matrices",

author = "Qiang Ye",

year = "1991",

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language = "English",

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T1 - A convergencea nalysis for nonsymmetric lanczos algorithms

AU - Ye, Qiang

PY - 1991/4

Y1 - 1991/4

N2 - A convergence analysis for the nonsymmetric Lanczos algorithm is presented. By using a tridiagonal structure of the algorithm, some identities concerning Ritz values and Ritz vectors are established and used to derive approximation bounds. In particular, the analysis implies the classical results for the symmetric Lanczos algorithm.

AB - A convergence analysis for the nonsymmetric Lanczos algorithm is presented. By using a tridiagonal structure of the algorithm, some identities concerning Ritz values and Ritz vectors are established and used to derive approximation bounds. In particular, the analysis implies the classical results for the symmetric Lanczos algorithm.

KW - Convergence bound

KW - Lanczos algorithm

KW - Tridiagonal matrices

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U2 - 10.1090/S0025-5718-1991-1068826-4

DO - 10.1090/S0025-5718-1991-1068826-4

M3 - Article

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SN - 0025-5718

VL - 56

SP - 677

EP - 691

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 194

ER -

A convergencea nalysis for nonsymmetric lanczos algorithms

Abstract

Keywords

ASJC Scopus subject areas

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