Preprint 18/2004

Approximation of integral operators by H2-matrices with adaptive bases

Steffen Börm

Contact the author: Please use for correspondence this email.
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
MSC-Numbers: 45B05, 65N38, 65F30
Keywords and phrases: hierarchical matrices, data-sparse approximation, nested bases
Download full preprint: PDF (262 kB), PS ziped (225 kB)

Abstract:
formula9-matrices can be used to construct efficient approximations of discretized integral operators. The formula9-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.

19.04.2013, 01:41