On numerical analysis of conjugate gradient method
type: Item
instance of: scholarly article
title: On numerical analysis of conjugate gradient method
zbMATH Open document ID: 0802.65037
DOI: 10.1007/BF03167286
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1994-12-11T00:00:00Z
review text: The author spoils several pages by telling us what we should know since our first numerical analysis course: successive overrelaxation (SOR) methods, Banach's fixed point theorem and error analysis conclusions from it, the conjugate gradient method. Stopping criteria are developed using the well-known error estimates mentioned. More than half of the paper is devoted to numerical experiments. They compare line SOR with conjugate gradient methods with different preconditioning. The results show very different behaviour of the methods for standard and non-standard problems with discontinuous coefficients.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 597561
zbMATH Keywords: line SOR method
zbMATH Keywords: stopping criteria
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: error estimates
zbMATH Keywords: preconditioning
author: Zbigniew I. Woźnicki
MaRDI profile type: Publication
cites work: Q3909906
cites work: Methods of conjugate gradients for solving linear systems
cites work: The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
cites work: An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
cites work: Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems
cites work: Block Preconditioning for the Conjugate Gradient Method
cites work: Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
full work available at URL: https://doi.org/10.1007/bf03167286
OpenAlex ID: W2105041011
description: scientific article; zbMATH DE number 597561