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

Dmytryshyn, Andrii; Fasi, Massimiliano; Gulliksson, Mårten

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Authors

Andrii Dmytryshyn

Mårten Gulliksson



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
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 435
Article Number 127458
DOI https://doi.org/10.1016/j.amc.2022.127458

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