SIAM Journal on Scientific Computing, Volume 42, Issue 2, Page C43-C68, January 2020.
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.

中文翻译：

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hm-toolbox：用于HODLR和HSS矩阵的MATLAB软件

SIAM科学计算杂志，第42卷，第2期，第C43-C68页，2020年1月。
具有分层低秩结构的矩阵（包括HODLR和HSS矩阵）构成了开发快速算法以解决大规模问题的通用工具。尽管用于此类矩阵的现有软件包通常专注于线性系统，但它们的应用范围实际上要广得多，并且包括例如矩阵函数和特征值问题。在这项工作中，我们提出了一个新的名为hm-toolbox的MATLAB工具箱，该工具箱包含了广泛的功能，涵盖了HODLR和HSS矩阵的广泛工具，这是现有软件无法比拟的。尽管我们的工具箱主要基于可在文献中找到的算法，但它还包含一些新算法以及新颖的辅助功能。由于完全基于MATLAB，因此我们的实现并不追求最佳性能。不过，它保持了低等级的低级矩阵的良好复杂性，同时提供了一种方便的原型设计和算法实验方法。许多应用程序说明了hm-toolbox的用法。