Year: 2017
Author: Yifen Ke, Changfeng Ma
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 5 : pp. 620–641
Abstract
In this paper, we present two alternating direction methods for the solution and best approximate solution of the Sylvester-type matrix equation $AXB+CX^⊤D=E$ arising in the control theory, where $A,B,C,D$ and $E$ are given matrices of suitable sizes. If the matrix equation is consistent (inconsistent), then the solution (the least squares solution) can be obtained. Preliminary convergence properties of the proposed algorithms are presented. Numerical experiments show that the proposed algorithms tend to deliver higher quality solutions with less iteration steps and CPU time than some existing algorithms on the tested problems.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1608-m2015-0430
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 5 : pp. 620–641
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Sylvester-type matrix equation Alternating direction method The least squares solution Best approximate solution.
Author Details
-
On the solutions of a class of tensor equations
Xu, Xiangjian | Wang, Qing-WenLinear and Multilinear Algebra, Vol. 70 (2022), Iss. 21 P.6141
https://doi.org/10.1080/03081087.2021.1948492 [Citations: 1] -
Iterative algorithms for discrete-time periodic Sylvester matrix equations and its application in antilinear periodic system
Wang, Wenli | Song, CaiqinApplied Numerical Mathematics, Vol. 168 (2021), Iss. P.251
https://doi.org/10.1016/j.apnum.2021.06.006 [Citations: 20] -
Gradient-based iterative approach for solving constrained systems of linear matrix equations
Shirilord, Akbar | Dehghan, MehdiComputational and Applied Mathematics, Vol. 43 (2024), Iss. 4
https://doi.org/10.1007/s40314-024-02687-6 [Citations: 0] -
On a transformation of the ∗-congruence Sylvester equation for the least squares optimization
Satake, Yuki | Sogabe, Tomohiro | Kemmochi, Tomoya | Zhang, Shao-LiangOptimization Methods and Software, Vol. 35 (2020), Iss. 5 P.974
https://doi.org/10.1080/10556788.2020.1734004 [Citations: 1] -
Least squares solution of the quaternion Sylvester tensor equation
Wang, Qing-Wen | Xu, Xiangjian | Duan, XuefengLinear and Multilinear Algebra, Vol. 69 (2021), Iss. 1 P.104
https://doi.org/10.1080/03081087.2019.1588848 [Citations: 20] -
Iterative algorithm for a generalized matrix equation with momentum acceleration approach and its convergence analysis
Shirilord, Akbar | Dehghan, MehdiJournal of the Franklin Institute, Vol. 361 (2024), Iss. 12 P.107021
https://doi.org/10.1016/j.jfranklin.2024.107021 [Citations: 0] -
Solving a system of complex matrix equations using a gradient-based method and its application in image restoration
Shirilord, Akbar | Dehghan, MehdiNumerical Algorithms, Vol. (2024), Iss.
https://doi.org/10.1007/s11075-024-01856-2 [Citations: 0] -
Iterative method for constrained systems of conjugate transpose matrix equations
Shirilord, Akbar | Dehghan, MehdiApplied Numerical Mathematics, Vol. 198 (2024), Iss. P.474
https://doi.org/10.1016/j.apnum.2024.01.016 [Citations: 1] -
An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations
Chen, Xuesong | Chen, ZebinJournal of the Franklin Institute, Vol. 358 (2021), Iss. 10 P.5513
https://doi.org/10.1016/j.jfranklin.2021.05.012 [Citations: 3] -
Extending BiCG and BiCR methods to solve the Stein tensor equation
Xu, Xiangjian | Wang, Qing-WenComputers & Mathematics with Applications, Vol. 77 (2019), Iss. 12 P.3117
https://doi.org/10.1016/j.camwa.2019.01.024 [Citations: 25]