Stabilised rounded addition of hierarchical matrices

Mario Bebendorf, and Wolfgang Hackbusch
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Submission date: 12. Jan. 2007
Pages: 17
published in: Numerical linear algebra with applications, 14 (2007) 5, p. 407-423 
DOI number (of the published article): 10.1002/nla.525
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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 definitness 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.