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


Authors: Ivan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij
Journal: Math. Comp. 74 (2005), 681-708
MSC (2000): Primary 65F50, 65F30; Secondary 15A24, 15A99
Published electronically: August 23, 2004
MathSciNet review: 2114643
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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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Additional Information

Ivan P. Gavrilyuk
Affiliation: Berufsakademie Thüringen, Am Wartenberg 2, D-99817 Eisenach, Germany
Email: ipg@ba-eisenach.de

Wolfgang Hackbusch
Affiliation: Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany
Email: wh@mis.mpg.de

Boris N. Khoromskij
Affiliation: Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany
Email: bokh@mis.mpg.de

DOI: https://doi.org/10.1090/S0025-5718-04-01703-X
Keywords: Operator-valued function, data-sparse approximation, elliptic operator, $\mathcal{H}$-matrices
Received by editor(s): April 10, 2003
Published electronically: August 23, 2004
Article copyright: © Copyright 2004 American Mathematical Society