Stabilized rounded addition of hierarchical matrices

The efficiency of hierarchical matrices is based on the approximate evaluation of usual matrix operations. The introduced approximation error may, however, lead to a loss of important matrix properties. In this article we present a technique which preserves the positive definiteness of a matrix inde...

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Bibliographic Details
Published inNumerical linear algebra with applications Vol. 14; no. 5; pp. 407 - 423
Main Authors Bebendorf, M., Hackbusch, W.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.06.2007
Subjects
hierarchical matrices
stabilized approximate operations
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Summary:The efficiency of hierarchical matrices is based on the approximate evaluation of usual matrix operations. The introduced approximation error may, however, lead to a loss of important matrix properties. In this article we present a technique which preserves the positive definiteness of a matrix independently of the approximation quality. The importance of this technique is illustrated by an elliptic mixed boundary value problem with tiny Dirichlet part. Copyright © 2007 John Wiley & Sons, Ltd.
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ISSN:1070-5325
1099-1506
DOI:10.1002/nla.525