A comparative study of sparse approximate inverse preconditioners
type: Item
instance of: scholarly article
title: A comparative study of sparse approximate inverse preconditioners
zbMATH Open document ID: 0949.65043
DOI: 10.1016/S0168-9274(98)00118-4
author: Michele Benzi
author: Miroslav Tuma
published in: Applied Numerical Mathematics
publication date: 2000-11-21T00:00:00Z
review text: Numerical analysis practitioners are well aware of the increasing number of preconditioners available to solve the large linear systems that arise in many applications. They also encounter difficulties when it comes to decide which approach might prove more suitable for a specific problem in a given computational environment. After more than two decades since the pioneering paper by \textit{J. A. Meijerink} and \textit{H. A. van der Vorst} [Math. Comput. 31, 148-162 (1977; Zbl 0349.65020)], introducing the subject via the incomplete factorizations, here is a systematic attempt to organize those newcomers based on sparse approximate inverses, which also takes into account the differences that may arise between serial and parallel processing. From the start the authors take the view that sparse approximate inverse methods will become an increasingly important tool for high-performance preconditioning of large linear systems. Accordingly, these methods are carefully classified into three main groups, which are generically described as methods based on Frobenius norm minimization, methods with factorized sparse approximate inverses, and those which consider incomplete factorizations followed by an approximate inversion of the incomplete factors. A large number of numerical experiments have been carried out on both symmetric positive definite systems and nonsymmetric ones. The systems have been taken from well-known benchmarks and cover a wide spectrum of problems arising from applications such as structural analysis, oil reservoir simulation, circuit modelling and power system network. The approximate inverse methods are thoroughly compared with the classic preconditioning methods based on incomplete factorizations and also polynomial preconditioning based on truncated Neumann series is considered. As general heuristical conclusions it is stated that on circuit problems, approximate inverse techniques can be more effective than incomplete factorizations, while the rever…
reviewed by: Juan Pedro Milaszewicz
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1311339
zbMATH Keywords: sparse linear systems
zbMATH Keywords: incomplete factorizations
zbMATH Keywords: approximate inverse preconditioners
zbMATH Keywords: approximate inverse methods
zbMATH Keywords: numerical experiments
describes a project that uses: LAPACK
describes a project that uses: SparseMatrix
describes a project that uses: Harwell-Boeing sparse matrix collection
describes a project that uses: LINSOL
MaRDI profile type: Publication
full work available at URL: s0168-9274(98)00118-4
OpenAlex ID: W2156588317
description: scientific article; zbMATH DE number 1311339