Hierarchical Kronecker tensor-product approximation to a class of nonlocal operators in high dimensions

Content Provider	Semantic Scholar
Author	Hackbusch, Wolfgang Khoromskij, Boris N.
Copyright Year	2004
Abstract	The class of H-matrices allows an approximate matrix arithmetic with almost linear complexity. The combination of the hierarchical and tensor-product format offers the opportunity for efficient data-sparse representations of integral operators and the inverse of elliptic operators in higher dimensions (cf. [19], [7]). In the present paper, we apply the H-matrix techniques combined with the Kronecker tensorproduct approximation to represent integral operators as well as certain functions F(A) of a discrete elliptic operator A in a hypercube (0, 1) ∈ R in the case of a high spatial dimension d. In particular, we approximate the functions A−1 and sign(A) of a finite difference discretisations A ∈ RN×N with rather general location of the spectrum. The asymptotic complexity of our data-sparse representations can be estimated by O(np log n), p = 1, 2, with q independent of d, where n = N is the dimension of the discrete problem in one space direction. AMS Subject Classification: 65F50, 65F30, 46B28, 47A80
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://www.mis.mpg.de/preprints/2004/preprint2004_16.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article