Least-squares symmetric and skew-symmetric solutions of the generalized Sylvester matrix equation ∑i=1sAiXBi+∑j=1tCjYDj=E

Yongxin Yuan and Kezheng Zuo

Applied Mathematics and Computation, 2015, vol. 265, issue C, 370-379

Abstract: The generalized Sylvester matrix equation ∑i=1sAiXBi+∑j=1tCjYDj=E with unknown matrices X and Y is encountered in many system and control applications. In this paper, a direct method is established to solve the least-squares symmetric and skew-symmetric solutions of the equation by using the Kronecker product and the generalized inverses and, the expression of the solution set S are provided. Moreover, an optimal approximation between a given matrix pair and the affine subspace S is discussed, and an explicit formula for the unique optimal approximation solution is presented. Finally, two numerical examples are given which demonstrate that the introduced algorithm is quite efficient.

Keywords: Generalized Sylvester matrix equation; Symmetric solution; Skew-symmetric solution; Least-squares solution; Optimal approximation (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:370-379

DOI: 10.1016/j.amc.2015.05.035

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