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

Gavrilyuk, Ivan; Hackbusch, Wolfgang; Khoromskij, Boris

doi:10.1090/S0025-5718-04-01703-X

Data-sparse approximation to a class of operator-valued functions
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by Ivan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij;

Math. Comp. 74 (2005), 681-708

DOI: https://doi.org/10.1090/S0025-5718-04-01703-X

Published electronically: August 23, 2004

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Abstract:

In earlier papers we developed a method for the data-sparse approximation of the solution operators for elliptic, parabolic, and hyperbolic PDEs 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 the operator-valued functions generated by an elliptic operator $\mathcal {L}$.

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