Hierarchical matrices based on a weak admissibility criterion
type: Item
instance of: scholarly article
title: Hierarchical matrices based on a weak admissibility criterion
zbMATH Open document ID: 1063.65035
author: Wolfgang Hackbusch
author: Boris N. Khoromskij
author: Ronald Kriemann
published in: Computing
publication date: 2005-02-23T00:00:00Z
review text: The class of \(\mathcal{H}\)-matrices was developed to approximate nonlocal operator equations in a cheap way. Not only are those matrices sparse but they allow their computation with almost linear complexity only. In particular, \(\mathcal{H}\)-matrices are very well suited for the approximation of integral equations. However, while matrix-vector multiplication is very cheap, matrix-matrix operations are much more expensive. This fact comes mainly from a large constant which is usually surpressed by the \(\mathcal{O}\)-notation used in the comlexity estimates. This may be achieved by a simpler block partitioning in the hierarchy of the matrices and this is the main topic of the paper under review. However, allowing a more relaxed admissibility condition which leads to a simpler partitioning the authors come up with the conjecture that the complexity will stay nearly the same. This conjecture leads to the definition of new families of matrices which may play a crucial role in the arithmetic of \(\mathcal{H}\)-matrices.
reviewed by: Thomas Sonar
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 2138067
zbMATH Keywords: \(\mathcal{H}\)-matrices
zbMATH Keywords: admissibility criteria
zbMATH Keywords: matrix-vector multiplication
zbMATH Keywords: matrix-matrix operations
zbMATH Keywords: block partitioning
zbMATH Keywords: complexity
MaRDI profile type: Publication
full work available at URL: s00607-004-0080-4
OpenAlex ID: W1976016599
DOI: 10.1007/S00607-004-0080-4
description: scientific article; zbMATH DE number 2138067