Wavelet sparse approximate inverse preconditioners
type: Item
instance of: scholarly article
title: Wavelet sparse approximate inverse preconditioners
zbMATH Open document ID: 0891.65048
DOI: 10.1007/BF02510244
published in: BIT
publication date: 1997-11-13T00:00:00Z
review text: The authors are interested in solving large sparse problems of the form \(Ax= b\) using sparse approximate inverse preconditioners. This amounts to first solving \(AMy= b\) and then computing \(x= My\). The aim is to choose \(M\) such that it has as much sparsity as possible while \(AM\) is still an approximation to the identity matrix. The main idea in the present paper is to represent \(A\) in a different basis in which \(A^{-1}\) has a sparse approximation. Specifically, if \(A^{-1}\) presents some piecewise smoothness then one uses a wavelet transformation to convert this smoothness into small wavelet coefficients. The authors compare this idea to that of a hierarchical basis preconditioner (to which it is closely related) and present a large number of interesting numerical experiments. The weak points of the method are also fairly discussed with suggestions for future work.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65T50
zbMATH DE Number: 1087022
zbMATH Keywords: large sparse problems
zbMATH Keywords: inverse preconditioners
zbMATH Keywords: wavelet transformation
zbMATH Keywords: hierarchical basis preconditioner
zbMATH Keywords: numerical experiments
Wikidata QID: Q57397394
author: Tony F. Chan
author: Wei-Pai Tang
author: Wing-Lok Wan
reviewed by: Willy J. F. Govaerts
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1087022