Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications

Abstract

Matrices with low-rank off-diagonal blocks are a versatile tool to perform matrix compression and to speed up various matrix operations, such as the solution of linear systems. Often, the underlying block partitioning is described by a hierarchical partitioning of the row and column indices, thus giving rise to hierarchical low-rank structures. The goal of this chap- ter is to provide a brief introduction to these techniques, with an emphasis on linear algebra aspects.