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• W122023075 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" @default.
• W122023075 created "2016-06-24" @default.
• W122023075 creator A5043445843 @default.
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• W122023075 date "2004-04-13" @default.
• W122023075 modified "2023-09-23" @default.
• W122023075 title "Hierarchical Kronecker tensor-product approximation to a class of nonlocal operators in high dimensions" @default.
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