The dynamical functional particle method for multi-term linear matrix equations

Dmytryshyn, Andrii and Fasi, Massimiliano and Gulliksson, Mårten (2021) The dynamical functional particle method for multi-term linear matrix equations. [MIMS Preprint]

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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 or negative definite coefficients. In numerical experiments, our MATLAB implementation outperforms existing methods for the solution of generalized 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.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Mr Massimiliano Fasi
Date Deposited: 31 Jul 2022 09:49
Last Modified: 31 Jul 2022 09:49
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2864

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