Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
type: Item
instance of: scholarly article
title: Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
zbMATH Open document ID: 1071.65032
author: Iwan Gawriljuk
author: Boris N. Khoromskij
author: Wolfgang Hackbusch
published in: Computing
publication date: 2005-05-12T00:00:00Z
review text: It is well known that integral operators in higher dimensions can be approximated by using the so-called hierarchical Kronecker tensor-product (HKT) format. The authors construct and analyze an HKT approximation for the general class of strongly positive operators defined as a sum of low-dimensional commutative operators and combine tensor product representation that includes one-dimensional operators. They develop a data sparse HKT approximation of the inverse of an elliptic operator as well as to the solution operator of the matrix Lyapunov-Sylvester equation. The approximation can be interpreted as an extension of the widely used fast Fourier transform.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 47A80
zbMATH DE Number: 2167500
zbMATH Keywords: hierarchical matrices
zbMATH Keywords: Kronecker tensor-product
zbMATH Keywords: integral operators
zbMATH Keywords: strongly positive operators
zbMATH Keywords: Lyapunov-Sylvester matrix equation
zbMATH Keywords: fast Fourier transform
reviewed by: R. P. Tewarson
MaRDI profile type: Publication
full work available at URL: s00607-004-0086-y
OpenAlex ID: W2028247581
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DOI: 10.1007/S00607-004-0086-Y
description: scientific article; zbMATH DE number 2167500