Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators

Authors:
W. Hackbusch;N. Khoromskij
Affiliations:
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22-26, 04103, Leipzig, Germany;Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22-26, 04103, Leipzig, Germany
Venue:
Computing
Year:
2006

Citing 0
Cited 5

A structured low-rank wavelet solver for the Ornstein-Zernike integral equation

Computing
Tensor-product approximation to operators and functions in high dimensions

Journal of Complexity
Kronecker product approximation of demagnetizing tensors for micromagnetics

Journal of Computational Physics
Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition

SIAM Journal on Matrix Analysis and Applications
Tensor-Train Decomposition

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

This article is the second part continuing Part I [16]. 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 (0,1) d ∈ ℝ d in the case of a high spatial dimension d. We focus on the approximation of the operator-valued functions A−σ, σ0, and sign (A) for a class of finite difference discretisations A ∈ ℝN×N. The asymptotic complexity of our data-sparse representations can be estimated by ** (np log qn), p = 1, 2, with q independent of d, where n=N1/d is the dimension of the discrete problem in one space direction.