Data-sparse approximation of a class of operator-valued functions
Ivan P. Gavrilyuk, Wolfgang Hackbusch, and Boris N. Khoromskij
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Submission date: 10. Mar. 2003 (revised version: February 2004)
published in: Mathematics of computation, 74 (2005) 250, p. 681-708
MSC-Numbers: 65F50, 65F30
Keywords and phrases: data-sparse approximation, operator-valued functions
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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.