The dynamical functional particle method for the generalized Sylvester equation

Dmytryshyn, Andrii and Fasi, Massimiliano and Gulliksson, Mårten (2021) The dynamical functional particle method for the generalized Sylvester equation. [MIMS Preprint]

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Abstract

Recent years have seen a renewal of interest in the study of generalized Sylvester equations, which have come to play a role in a number or applications. Here we consider the solution of such equations by means of the dynamical functional particle method, an iterative technique that relies on the construction and 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 generalized Sylvester equations with Hermitian positive definite coefficients. Our numerical experiments show that the new implementations outperform existing methods for the solution of generalized Sylvester equations, and can be faster and more accurate than the Bartels–Stewart algorithm for the solution of the Sylvester equation AX − XB = C, when A and B are well conditioned and have very different order.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Mr Massimiliano Fasi
Date Deposited: 26 Feb 2021 09:44
Last Modified: 26 Feb 2021 09:44
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2804

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