Approximation of integral operators by ²-matrices with adaptive bases

Steffen Börm

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Submission date: 15. Apr. 2004 (revised version: December 2004)
Pages: 24
published in: Computing, 74 (2005) 3, p. 249-271 
DOI number (of the published article): 10.1007/s00607-004-0106-y
Bibtex
MSC-Numbers: 45B05, 65N38, 65F30
Keywords and phrases: hierarchical matrices, data-sparse approximation, nested bases
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Abstract:
-matrices can be used to construct efficient approximations of discretized integral operators. The -matrix approximation can be constructed efficiently by interpolation, Taylor or multipole expansion of the integral kernel function, but the resulting representation requires a large amount of storage.

In order to improve the efficiency, local Schur decompositions can be used to eliminate redundant functions from an original approximation, which leads to a significant reduction of storage requirements and algorithmic complexity.