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The dynamical functional particle method for multi-term linear matrix equations
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DOI：10.1016/j.amc.2022.127458.png)
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摘要
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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.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
Keyword:
Linear matrix equation
Discrete functional particle method
Lyapunov equation
Sylvester equation
Generalized Sylvester equation
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3.4
论文数:
2.3W
被引数:
3.3W
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