 The dynamical functional particle method for multi-term linear matrix equationsAndrii Dmytryshyn, Massimiliano Fasi and Mårten Gulliksson Applied Mathematics and Computation, 2022, vol. 435, issue C 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. Keywords: Linear matrix equation; Discrete functional particle method; Lyapunov equation; Sylvester equation; Generalized Sylvester equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:435:y:2022:i:c:s009630032200532x DOI: 10.1016/j.amc.2022.127458 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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