On the purely algebraic data-sparse approximation of the inverse and the triangular factors of sparse matrices

The approximation of the inverse and the factors of the LU decomposition of general sparse matrices by hierarchical matrices is investigated. In this first approach, we present and motivate a new matrix partitioning algorithm which is based on the matrix graph by proving logarithmic‐linear complexit...

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Published inNumerical linear algebra with applications Vol. 18; no. 1; pp. 105 - 122
Main Authors Bebendorf, M., Fischer, T.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.01.2011
Subjects
Algebra
Algorithms
Approximation
fast methods
hierarchical matrices
Inverse
Mathematical analysis
Mathematical models
Partitioning
preconditioners
Sparse matrices
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Summary:The approximation of the inverse and the factors of the LU decomposition of general sparse matrices by hierarchical matrices is investigated. In this first approach, we present and motivate a new matrix partitioning algorithm which is based on the matrix graph by proving logarithmic‐linear complexity of the approximant in the case of bounded condition numbers. In contrast to the usual partitioning, the new algorithm allows to treat general grids if the origin of the sparse matrix is the finite element discretization of differential operators. Numerical examples indicate that the restriction to bounded condition numbers has only technical reasons. Copyright © 2010 John Wiley & Sons, Ltd.
Bibliography:ArticleID:NLA714
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DFG priority program SPP 1146 'Modellierung inkrementeller Umformverfahren'
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ISSN:1070-5325
1099-1506
1099-1506
DOI:10.1002/nla.714