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Selçuk Journal
of
Applied Mathematics
Summer-Autumn, 2000
Volume 1
Number 1
Research Center
of
Applied Mathematics
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SJAM
Summer-Autumn 2000, Volume 1 - Number 1
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Factorized Sparse Approximate Inverses for Preconditioning and Smoothing
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Thomas
Huckle |
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Institut für Informatik, Technische Universität München, D-80290
München, Germany;
email: huckle@in.tum.de
Received: 25 August 2000
To
Prof. Dr. Chr. Zenger 60-th birthday
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Summary
In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax=b is examined. The minimization of || AM-I || in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M.
For symmetric positive definite A and a given a priori pattern there exist methods for computing
factorized sparse approximate inverses L with LLT A-1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L. We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test
modifications of this method for computing factorized sparse approximate inverses that are suited for smoothing in multigrid solvers.
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Key
words
sparse linear systems, factorized sparse approximate inverses,
preconditioned conjugate gradients, smoother, multi-grid
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Mathematics Subject Classification (1991):
65F10,
65F50, 15A09, 15A23
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Article
in PS format (113 kb) |
Article in ZIP
format (44 kb) |
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