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The dynamical functional particle method for multi-term linear matrix equations
Örebro University, School of Science and Technology.ORCID iD: 0000-0001-9110-6182
Department of Computer Science, Durham University, Durham, UK.
Örebro University, School of Science and Technology. Orebro Univ, Sch Sci & Technol, S-70182 Orebro, Sweden..ORCID iD: 0000-0003-0332-2315
2022 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 435, article id 127458Article in journal (Refereed) Published
Abstract [en]

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 dy-namical 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 Hermi-tian positive definite or negative definite coefficients. In numerical experiments, our MAT -LAB 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.

Place, publisher, year, edition, pages
Elsevier, 2022. Vol. 435, article id 127458
Keywords [en]
Linear matrix equation, Discrete functional particle method, Lyapunov equation, Sylvester equation, Generalized Sylvester equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-101785DOI: 10.1016/j.amc.2022.127458ISI: 000863293600002Scopus ID: 2-s2.0-85135936262OAI: oai:DiVA.org:oru-101785DiVA, id: diva2:1704108
Funder
Swedish Research Council, 2021-05393Wenner-Gren Foundations, UPD2019-0067Available from: 2022-10-17 Created: 2022-10-17 Last updated: 2022-10-17Bibliographically approved

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Dmytryshyn, AndriiGulliksson, Mårten

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