Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
type: Item
instance of: scholarly article
title: Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
zbMATH Open document ID: 0662.65032
DOI: 10.1016/0024-3795(89)90285-1
author: Anne Greenbaum
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: For the Lanczos and conjugate-gradient algorithms it is shown that in the presence of roundoff the computed set of orthogonal polynomials are still orthogonal polynomials but with respect to a slighly different measure. This property is used to obtain information on the approximate eigenvalues computed by the Lanczos method and the rate of convergence of the perturbed conjugate-gradient algorithm.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 4082837
zbMATH Keywords: Lanczos method
zbMATH Keywords: conjugate-gradient method
zbMATH Keywords: error analysis
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: rate of convergence
reviewed by: Volker Mehrmann
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90285-1
OpenAlex ID: W2075351838
cites work: Comparison of splittings used with the conjugate gradient algorithm
cites work: Methods of conjugate gradients for solving linear systems
cites work: Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
cites work: The Lanczos Algorithm with Selective Orthogonalization
cites work: How to Make the Lanczos Algorithm Converge Slowly
Wikidata QID: Q126668091
description: scientific article; zbMATH DE number 4082837