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MiS Preprint

Hybrid Cross Approximation of Integral Operators

Steffen Börm and Lars Grasedyck


The efficient treatment of dense matrices arising, e.g., from the finite element discretisation of integral operators, requires special compression techniques. In this article we use the ${\cal H}$-matrix representation that approximates the dense stiffness matrix in admissible blocks (corresponding to subdomains where the underlying kernel function is smooth) by low rank matrices. The low rank matrices are assembled by a new hybrid algorithm (HCA) that has the same proven convergence as standard interpolation but also the same efficiency as the (heuristic) adaptive cross approximation (ACA).

MSC Codes:
45B05, 65N38, 68P05
hierarchical matrices, bem, interpolation

Related publications

2005 Repository Open Access
Steffen Börm and Lars Grasedyck

Hybrid cross approximation of integral operators

In: Numerische Mathematik, 101 (2005) 2, pp. 221-249