Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators
type: Item
instance of: scholarly article
title: Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators
zbMATH Open document ID: 1087.65050
author: Wolfgang Hackbusch
author: Boris N. Khoromskij
published in: Computing
publication date: 2006-03-02T00:00:00Z
review text: [For part I see ibid. 76, No.~3--4, 177--202 (2006; reviewed above).] The authors study the hierarchical Kronecker tensor product (HKT) representation of certain operators for low rank Kronecker product approximation to multi dimensional nonlocal operators. They apply H-matrix techniques combined with the Kronecker tensor product approximation to represent integral operators as well as of a discrete elliptic operator in a hypercube. They outline the main ideas how to construct the HKT approximations of the operator valued functions of the discrete elliptic operators with separable coefficients. In addition HKT representations of the multi-dimensional integral operators are given and an HKT approximation to the matrix valued function sign(\(A\)) of the operator \(A\) is addressed.
reviewed by: Seenith Sivasundaram
Mathematics Subject Classification ID: 65J05
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 47A80
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 65N38
zbMATH DE Number: 5009651
zbMATH Keywords: hierarchical matrices
zbMATH Keywords: Kronecker tensor product
zbMATH Keywords: sinc interpolation
zbMATH Keywords: sinc quadrature
zbMATH Keywords: integral operators
zbMATH Keywords: discrete elliptic operator
MaRDI profile type: Publication
full work available at URL: s00607-005-0145-z
OpenAlex ID: W2095121180
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DOI: 10.1007/S00607-005-0145-Z
description: scientific article; zbMATH DE number 5009651