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Research Article
Stabilized rounded addition of hierarchical matrices
Article first published online: 11 JAN 2007
DOI: 10.1002/nla.525
Copyright © 2007 John Wiley & Sons, Ltd.
1099-1506/asset/cover.gif?v=1&s=4c716168b1bef317e4ae1ebaac712130c9fe6913 "Numerical Linear Algebra with Applications")
Additional Information
How to Cite
Bebendorf, M. and Hackbusch, W. (2007), Stabilized rounded addition of hierarchical matrices. Numerical Linear Algebra with Applications, 14: 407–423. doi: 10.1002/nla.525
Publication History
- Issue published online: 16 APR 2007
- Article first published online: 11 JAN 2007
- Manuscript Accepted: 12 NOV 2006
- Manuscript Revised: 9 NOV 2006
- Manuscript Received: 19 JUL 2006
- Abstract
- References
- Cited By
Keywords:
- hierarchical matrices;
- stabilized approximate operations
Abstract
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.