Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors
type: Item
instance of: scholarly article
title: Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors
zbMATH Open document ID: 0625.65019
DOI: 10.1016/0378-4754(87)90062-0
author: Elias A. Lipitakis
author: D. J. Evans
published in: Mathematics and Computers in Simulation
publication date: 1987-01-01T00:00:00Z
review text: The authors consider several preconditioners for iterative solution methods. The preconditioners are based on incomplete direct methods. One method, called the generalized approximate inverse matrix technique, is based on a construction of the inverse of an \(n\times n\) matrix A starting from the factorization \(A=LU\), but without computing \(L^{-1}\) and \(U^{-1}\) explicitly. This method, and a variant based on retaining only some of the diagonals of the inverse, can be efficiently computed by diagonals on a vector or parallel processor. A second class of methods is based on Gauss-Jordan elimination and the resulting expression of \(A^{-1}\) as a product of simple matrices. The different methods in the class are determined by retention of different numbers of diagonals. Numerical results are presented for several different variations of these methods applied to the matrix arising from a ``2D-model problem''. The model problem is not described.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 4016029
zbMATH Keywords: preconditioning
zbMATH Keywords: LU-factorization
zbMATH Keywords: incomplete direct methods
zbMATH Keywords: generalized approximate inverse matrix technique
zbMATH Keywords: parallel processor
zbMATH Keywords: Gauss-Jordan elimination
reviewed by: Myron Sussman
MaRDI profile type: Publication
full work available at URL: 0378-4754(87)90062-0
OpenAlex ID: W2046444904
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description: scientific article; zbMATH DE number 4016029