The dynamical functional particle method for the generalized Sylvester equation

Abstract

Recent years have seen a renewal of interest in generalized Sylvester 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 generalized Sylvester equations with Hermitian positive 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