Preprint 30/2005

Low-Rank Kronecker Product Approximation to Multi-Dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators

Wolfgang Hackbusch and Boris N. Khoromskij

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Submission date: 14. Apr. 2005 (revised version: September 2005)
Pages: 19
published in: Computing, 76 (2006) 3/4, p. 203-225 
DOI number (of the published article): 10.1007/s00607-005-0145-z
Bibtex
MSC-Numbers: 65F50, 65F30, 46B28, 47A80
Keywords and phrases: hierarchical matrices, kronecker tensor-product, high spatial dimension, sinc interpolation, sinc quadrature
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Abstract:
This article is the second part continuing Part I. We apply the formula20-matrix techniques combined with the Kronecker tensor-product approximation to represent integral operators as well as certain functions F(A) of a discrete elliptic operator A in a hypercube formula26 in the case of a high spatial dimension d. We focus on the approximation of the operator-valued functions formula30, formula32, and formula34 for a class of finite difference discretisations formula36. The asymptotic complexity of our data-sparse representations can be estimated by formula38, p=1,2, with q independent of d, where formula46 is the dimension of the discrete problem in one space direction.

18.07.2014, 01:41