Adaptive low-rank approximation of collocation matrices

Abstract

This article deals with the solution of integral equations using collocation methods with almost linear complexity. This is done by generating a blockwise low-rank approximation to the system matrix. In contrast to fast multipole and panel clustering the proposed algorithm is based on only few entries from the original matrix. In this article the results concerning matrix approximation from [1] are generalized to collocation matrices and improved. Furthermore, we present a new algorithm for matrix partitioning that dramatically reduces the number of blocks generated.