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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
103/2002

Construction and Arithmetics of $\mathcal{H}$-Matrices

Lars Grasedyck and Wolfgang Hackbusch

Abstract

In previous papers a class of H-matrices was introduced which are data-sparse and allow an approximate matrix arithmetic of nearly optimal complexity. In this paper we analyse the complexity (storage, addition, multiplication and inversion) of the H-matrix arithmetics. Two criteria, the sparsity and idempotency, are sufficient to give the desired bounds. For standard finite element and boundary element applications we present a construction of an H-matrix format for which we can give explicit bounds for the sparsity and idempotency.

Received:
28.11.02
Published:
28.11.02
MSC Codes:
65F05, 65F30, 65F50
Keywords:
hierarchical matrices, data-sparse approximations, fast solvers, formatted matrix operations

Related publications

inJournal
2003 Repository Open Access
Lars Grasedyck and Wolfgang Hackbusch

Construction and arithmetics of \(\mathscr {H}\)-matrices

In: Computing, 70 (2003) 4, pp. 295-334