Composite adaptive procedure for solving large sparse linear systems
type: Item
instance of: scholarly article
title: Composite adaptive procedure for solving large sparse linear systems
zbMATH Open document ID: 0733.65019
DOI: 10.1016/0024-3795(91)90392-A
author: Tsun-Zee Mai
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: Adapted from the author's abstract: A large number of iterative algorithms for solving the matrix equation \(Ax=b\) have been developed in recent years. Some of these involve ``splitting parameters'', for example the relaxation parameter in the symmetric overrelaxation method, which are sensitive to their values. These can seldom be determined accurately in advance, and adaptive procedures are often used. A number of such procedures have been developed for finding the optimum splitting parameter for some iterative methods which are only applicable for some special cases. In the present paper a general adaptive procedure is given. This is similar to the ORTHONORM generalized conjugate gradient algorithm of \textit{D. M. Young} and \textit{K. C. Jea} [ibid. 34, 159-194 (1980; Zbl 0463.65025)] and is based on the minimization of an appropriate quadratic form using a unimodal search procedure. Computational algorithms are presented. There is a section on some numerical experiments for some problems which arise from solving partial differential equations. The author discusses briefly the parallelization of the methods.
reviewed by: D. Kershaw
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65N22
zbMATH DE Number: 4213318
zbMATH Keywords: large sparse linear systems
zbMATH Keywords: relaxation methods
zbMATH Keywords: splitting
zbMATH Keywords: parallel computation
zbMATH Keywords: iterative algorithms
zbMATH Keywords: symmetric overrelaxation
zbMATH Keywords: splitting parameter
zbMATH Keywords: conjugate gradient algorithm
zbMATH Keywords: Computational algorithms
zbMATH Keywords: numerical experiments
describes a project that uses: BRENT
MaRDI profile type: Publication
cites work: Q5657612
cites work: An Iterative Process for Optimizing Symmetric Successive Over-Relaxation
cites work: Q3909906
cites work: Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
cites work: An Incomplete Factorization Technique for Positive Definite Linear Systems
cites work: Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations
cites work: Q3819895
cites work: Q5604166
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description: scientific article; zbMATH DE number 4213318