hm-toolbox: Matlab software for HODLR and HSS matrices

TL;DR

The paper introduces hm-toolbox, a comprehensive Matlab software package for HODLR and HSS matrices, enabling fast algorithms for large-scale problems beyond linear systems, including matrix functions and eigenvalue computations.

Contribution

It provides a versatile Matlab toolbox with new algorithms and auxiliary functions for hierarchical low-rank matrices, expanding application scope and ease of prototyping.

Findings

Supports a wide range of applications including matrix functions and eigenvalue problems

Contains new algorithms and auxiliary functions not available in existing software

Maintains favorable complexity despite not being optimized for performance

Abstract

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, their scope of applications is in fact much wider and includes, for example, matrix functions and eigenvalue problems. In this work, we present a new Matlab toolbox called hm-toolbox, which encompasses this versatility with a broad set of tools for HODLR and HSS matrices, unmatched by existing software. While mostly based on algorithms that can be found in the literature, our toolbox also contains a few new algorithms as well as novel auxiliary functions. Being entirely based on Matlab, our implementation does not strive for optimal performance. Nevertheless, it maintains the favorable complexity of hierarchical low-rank matrices and offers, at the same time, a convenient way of prototyping and experimenting with algorithms. A number of applications illustrate the use of the hm-toolbox.