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MiS Preprint Repository

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
20/2003

Data-sparse approximation of a class of operator-valued functions

Ivan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij

Abstract

In previous papers a method for the data-sparse approximation of the solution operators for elliptic, parabolic and hyperbolic PDEs has been developed based on the Dunford-Cauchy representation to the operator-valued functions of interest combined with the hierarchical matrix approximation of the operator resolvents. In the present paper, we discuss how these techniques can be applied to approximate a hierarchy of operator-valued functions generated by an elliptic operator.

Received:
Mar 10, 2003
Published:
Mar 10, 2003
MSC Codes:
65F50, 65F30
Keywords:
data-sparse approximation, operator-valued functions

Related publications

inJournal
2005 Repository Open Access
Ivan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij

Data-sparse approximation to a class of operator-valued functions

In: Mathematics of computation, 74 (2005) 250, pp. 681-708