Numerical experiments with two approximate inverse preconditioners
type: Item
instance of: scholarly article
title: Numerical experiments with two approximate inverse preconditioners
zbMATH Open document ID: 0909.65027
DOI: 10.1007/BF02512364
author: Michele Benzi
author: Miroslav Tuma
published in: BIT
publication date: 1999-03-22T00:00:00Z
review text: The solution of a large and sparse system of linear equations \(Ax=b\) by iterative technique combined with preconditioner is considered. There is interest in an alternative form of preconditioning based on approximating the matrix inverse \(A^{-1}\). With this kind of preconditioner the computation can be performed in parallel. The most popular approach to approximate inverse preconditioning -- the SPAI algorithm -- is based on the idea of Frobenius norm minimization. Another approach for computing a factorized approximate inverse, suggested by the authors, is based on incomplete biconjugation. For general sparse matrices it is very difficult to prescribe the sparsity pattern in advance and so SPAI becomes very expensive. The construction of the AINV preconditioner does not require that the sparsity pattern be known in advance, and applicable to general sparse matrices. The authors present the results of numerical experiments aimed at comparing SPAI and AINV, performed on a set of sparse matrices. Results for a standard ILU preconditioner are also included. From the point of view of robustness and rates of convergence, SPAI and AINV are comparable and AINV is somewhat better on average.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1206830
zbMATH Keywords: sparse linear systems
zbMATH Keywords: preconditioned iterative methods
zbMATH Keywords: approximate inverses
zbMATH Keywords: SPAI
zbMATH Keywords: incomplete biconjugation
zbMATH Keywords: ILU
zbMATH Keywords: inverse preconditioning
zbMATH Keywords: numerical experiments
describes a project that uses: ISIS++
describes a project that uses: Harwell-Boeing sparse matrix collection
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1206830