Experiments with Krylov subspace methods on a massively parallel computer
type: Item
instance of: scholarly article
title: Experiments with Krylov subspace methods on a massively parallel computer
zbMATH Open document ID: 0810.65030
author: Martin Hanke
author: Marlis Hochbruck
author: Wilhelm Niethammer
published in: Applications of Mathematics
publication date: 1995-04-09T00:00:00Z
full work available at URL: https://eudml.org/doc/15764
review text: Different Krylov subspace iterative methods are compared in numerical experiments on the MasPar MP-1, a massively parallel computer with 16K processors. They include the conjugate gradient type methods BiCGStab of \textit{H. A. Van der Vorst} [SIAM J. Sci. Stat. Comput. 13, No. 2, 631-644 (1992; Zbl 0761.65023)] and GMRES of \textit{Y. Saad} and \textit{M. H. Schultz} [ibid. 7, 856-869 (1986; Zbl 0599.65018)], two- and four-step semiiterative methods as they are presented in the papers of \textit{T. A. Manteuffel} [Numer. Math. 28, 307-327 (1977; Zbl 0361.65024)] and \textit{W. Niethammer} and \textit{R. S. Varga} [ibid. 41, 177-206 (1983; Zbl 0509.65016)] and the hybrid GMRES-Richardson method. The above methods are also tested with preconditioning of the algebraic system matrix by the symmetric successive overrelaxation with red-black ordering and relaxation parameter \(W = 1\). The authors conclude that within their set of examples the semiiterative and hybrid methods are more attractive. They note also that the semiiterative method achieved the required accuracy fastest, however the a priori determination of the parameters, that are required for such methods is not always practical. The results of the experiment are influenced in particular by the fact that in parallel computers the cost of multiplication of matrix by vector is less than for scalar products.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 558557
zbMATH Keywords: parallel computation
zbMATH Keywords: Krylov subspace iterative methods
zbMATH Keywords: conjugate gradient type methods
zbMATH Keywords: BiCGStab
zbMATH Keywords: semiiterative methods
zbMATH Keywords: GMRES-Richardson method
zbMATH Keywords: preconditioning
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: red-black ordering
reviewed by: V.Gheorghiţă
MaRDI profile type: Publication
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OpenAlex ID: W135919330
DOI: 10.21136/AM.1993.104566
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description: scientific article; zbMATH DE number 558557