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MiS Preprint

Approximation of integral operators by ${\mathcal H}^2$-matrices with adaptive bases

Steffen Börm


${\mathcal H}^2$-matrices can be used to construct efficient approximations of discretized integral operators. The ${\mathcal H}^2$-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.

MSC Codes:
45B05, 65N38, 65F30
hierarchical matrices, data-sparse approximation, nested bases

Related publications

2005 Repository Open Access
Steffen Börm

Approximation of integral operators by \(\mathscr {H}^2\)-matrices with adaptive bases

In: Computing, 74 (2005) 3, pp. 249-271