Computers & Mathematics with Applications
Weighted least squares solutions to general coupled Sylvester matrix equations
Journal of Computational and Applied Mathematics
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Computers & Mathematics with Applications
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Computers & Mathematics with Applications
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Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
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Computers & Mathematics with Applications
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Computers & Mathematics with Applications
Iterative solutions to coupled Sylvester-conjugate matrix equations
Computers & Mathematics with Applications
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International Journal of Systems Science
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Computers & Mathematics with Applications
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Digital Signal Processing
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Computers & Mathematics with Applications
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Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
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Mathematical and Computer Modelling: An International Journal
An efficient algorithm for solving general coupled matrix equations and its application
Mathematical and Computer Modelling: An International Journal
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Solvability conditions and general solution for mixed Sylvester equations
Automatica (Journal of IFAC)
Efficient iterative solutions to general coupled matrix equations
International Journal of Automation and Computing
Developing Bi-CG and Bi-CR methods to solve generalized Sylvester-transpose matrix equations
International Journal of Automation and Computing
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In this paper we study coupled matrix equations, which are encountered in many systems and control applications. First, we extend the well-known Jacobi and Gauss--Seidel iterations and present a large family of iterative methods, which are then applied to develop iterative solutions to coupled Sylvester matrix equations. The basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle. Next, we generalize the Sylvester equations to general coupled matrix equations, and propose a gradient-based iterative algorithm for the solutions, using a block-matrix inner product---the star $(\star)$ product; we prove that the iterative algorithm always converges to the (unique) solutions for any initial values. One advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods. Finally, we test the algorithms and show their effectiveness using numerical examples.