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Stabilized rounded addition of hierarchical matrices
Author(s) -
Bebendorf M.,
Hackbusch W.
Publication year - 2007
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.525
Subject(s) - mathematics , matrix (chemical analysis) , positive definiteness , dirichlet distribution , boundary value problem , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , positive definite matrix , materials science , physics , quantum mechanics , composite material
The efficiency of hierarchical matrices is based on the approximate evaluation of usual matrix operations. The introduced approximation error may, however, lead to a loss of important matrix properties. In this article we present a technique which preserves the positive definiteness of a matrix independently of the approximation quality. The importance of this technique is illustrated by an elliptic mixed boundary value problem with tiny Dirichlet part. Copyright © 2007 John Wiley & Sons, Ltd.