Solving a large dense linear system by adaptive cross approximation

Authors:
Katrijn Frederix;Marc Van Barel
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven (Heverlee), Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven (Heverlee), Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

An efficient algorithm for the direct solution of a linear system associated with the discretization of boundary integral equations (in two dimensions) is described without having to compute the complete matrix of the linear system. This algorithm is based on the unitary-weight representation, for which a new construction based on adaptive cross approximation is proposed. This low rank approximation uses only a small part of the entries to construct the adaptive cross representation, and therefore the linear system can be solved efficiently.