Mathematics of Computation

Author(s): Ivan P. Gavrilyuk; Wolfgang Hackbusch; Boris N. Khoromskij.
Journal: Math. Comp. 74 (2005), 681-708.
MSC (2000): Primary 65F50, 65F30; Secondary 15A24, 15A99
Posted: 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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Retrieve articles in Mathematics of Computation with MSC (2000): 65F50, 65F30, 15A24, 15A99

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: 10.1090/S0025-5718-04-01703-X
PII: S 0025-5718(04)01703-X
Keywords: Operator-valued function, data-sparse approximation, elliptic operator, $\mathcal{H}$-matrices
Received by editor(s): April 10, 2003
Posted: August 23, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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