Lanczos maximal algorithm for unsymmetric eigenvalue problems
type: Item
instance of: scholarly article
title: Lanczos maximal algorithm for unsymmetric eigenvalue problems
zbMATH Open document ID: 0716.65030
DOI: 10.1016/0168-9274(91)90061-4
author: Mohamed Khelifi
published in: Applied Numerical Mathematics
publication date: 1991-01-01T00:00:00Z
review text: The look-ahead Lanczos (LAL) algorithm has been suggested by \textit{B. N. Parlett}, \textit{D. R. Taylor} and \textit{Z. A. Liu} [Math. Comput. 44, 105- 124 (1985; Zbl 0564.65022)] to deal with some breakdowns of the standard Lanczos algorithm for the solution of the eigenvalue problems. The author presents a modification of the LAL algorithm which maximizes the lower bound of \(p_ i^ Tq_ i\), where \(p_ i\) and \(q_ i\) are vectors obtained by some normalization of those generated by the Lanczos algorithm. Then it is shown that the algorithm minimizes an error estimate based on a result by \textit{W. Kahan}, \textit{B. N. Parlett}, and \textit{E. Jiang} [SIAM J. Numer. Anal. 19, 470-484 (1982; Zbl 0483.65024)]. The relation of the algorithm to Arnoldi's method is explained. The paper is supplied with results of numerical experiments.
reviewed by: Z. Dostál
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 4180656
zbMATH Keywords: maximal algorithm
zbMATH Keywords: unsymmetric eigenvalue problems
zbMATH Keywords: look-ahead Lanczos algorithm
zbMATH Keywords: error estimate
zbMATH Keywords: Arnoldi's method
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: 0168-9274(91)90061-4
OpenAlex ID: W2035200196
Wikidata QID: Q126401684
cites work: Q5185900
cites work: Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
cites work: The QR algorithm for real Hessenberg matrices
cites work: A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
cites work: Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
cites work: Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems
cites work: Q5674306
description: scientific article; zbMATH DE number 4180656