Data-sparse approximation to a class of operator-valued functions |
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| Authors: | Ivan P. Gavrilyuk Wolfgang Hackbusch Boris N. Khoromskij. |
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| Affiliation: | Berufsakademie Thüringen, Am Wartenberg 2, D-99817 Eisenach, Germany ; Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany ; Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany |
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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  . |
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| Keywords: | Operator-valued function data-sparse approximation elliptic operator $mathcal{H}$-matrices |
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