Data-sparse approximation of non-local operators by H2-matrices

Börm, Steffen (2007) Data-sparse approximation of non-local operators by H2-matrices Linear algebra and its applications, 422 . pp. 380-403. DOI 10.1016/j.laa.2006.10.021.

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Many of today’s most efficient numerical methods are based on multilevel decompositions: The multigrid algorithm is based on a hierarchy of grids, wavelet techniques use a hierarchy of basis functions, while fast panel-clustering and multipole methods employ a hierarchy of clusters.

The high efficiency of these methods is due to the fact that the hierarchies are nested, i.e., that the information present on a coarser level is also present on finer levels, thus allowing efficient recursive algorithms.

H2-matrices employ nested local expansion systems in order to approximate matrices in optimal (or for some problem classes at least optimal up to logarithmic factors) order of complexity. This paper presents a criterion for the approximability of general matrices in the H2-matrix format and an algorithm for finding good nested expansion systems and constructing the approximation efficiently.

Document Type: Article
Research affiliation: Kiel University
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
DOI etc.: 10.1016/j.laa.2006.10.021
ISSN: 0024-3795
Projects: Future Ocean
Date Deposited: 14 Apr 2011 07:33
Last Modified: 28 Sep 2017 13:24

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