The Dynamical Functional Particle Method for Multi-Term Linear Matrix Equations

Dmytryshyn, Andrii; Fasi, Massimiliano; Gulliksson, Mårten

Abstract

Recent years have seen a renewal of interest in multi-term linear matrix equations, as these have come to play a role in a number of important applications. Here, we consider the solution of such equations by means of the dynamical functional particle method, an iterative technique that relies on the numerical integration of a damped second order dynamical system. We develop a new algorithm for the solution of a large class of these equations, a class that includes, among others, all linear matrix equations with Hermitian positive definite or negative definite coefficients. In numerical experiments, our MATLAB implementation outperforms existing methods for the solution of multi-term Sylvester equations. For the Sylvester equation AX + XB = C, in particular, it can be faster and more accurate than the built-in implementation of the Bartels–Stewart algorithm, when A and B are well conditioned and have very different size.

Citation

Dmytryshyn, A., Fasi, M., & Gulliksson, M. (2022). The Dynamical Functional Particle Method for Multi-Term Linear Matrix Equations. Applied Mathematics and Computation, 435, Article 127458. https://doi.org/10.1016/j.amc.2022.127458

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2022
• Online Publication Date: Aug 14, 2022
• Publication Date: Dec 15, 2022
• Deposit Date: Aug 14, 2022
• Publicly Available Date: Sep 15, 2022
• Journal: Applied Mathematics and Computation
• Print ISSN: 0096-3003
• Electronic ISSN: 1873-5649
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 435
• Article Number: 127458
• DOI: https://doi.org/10.1016/j.amc.2022.127458
• Public URL: https://durham-repository.worktribe.com/output/1193885