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)
published in: Computing, 76 (2006) 3/4, p. 203-225
DOI number (of the published article): 10.1007/s00607-005-0145-z
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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This article is the second part continuing Part I. We apply the -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 in the case of a high spatial dimension d. We focus on the approximation of the operator-valued functions , , and for a class of finite difference discretisations . The asymptotic complexity of our data-sparse representations can be estimated by , p=1,2, with q independent of d, where is the dimension of the discrete problem in one space direction.