Recompression techniques for adaptive cross approximation

Abstract

The adaptive cross approximation method (ACA) generates low-rank approximations to suitable m× n sub-blocks of discrete integral formulations of elliptic boundary value problems. A characteristic property is that the approximation, which requires k(m+ n), k ∼ | log e|∗, units of storage, is generated in an adaptive and purely algebraic manner using only few of the matrix entries. In this article we present further recompression techniques which are based on ACA and bring the required amount of storage down to sublinear order kk′, where k′ depends logarithmically on the accuracy of the approximation but is independent of the matrix size. The additional compression is due to a certain smoothness of the vectors generated by ACA.