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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
4/2007

Stabilised rounded addition of hierarchical matrices

Mario Bebendorf and Wolfgang Hackbusch

Abstract

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 definitness 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.

Received:
Jan 12, 2007
Published:
Jan 12, 2007

Related publications

inJournal
2007 Repository Open Access
Mario Bebendorf and Wolfgang Hackbusch

Stabilized rounded addition of hierarchical matrices

In: Numerical linear algebra with applications, 14 (2007) 5, pp. 407-423