Approximation of Integral Operators by [Hierarchical]^sup 2^-Matrices with Adaptive Bases

Abstract

[Hierarchical]^sup 2^-matrices can be used to construct efficient approximations of discretized integral operators. The [Hierarchical]^sup 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. [PUBLICATION ABSTRACT]