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