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International Journal of Systems Science Volume 43, 2012 - Issue 8
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Original Articles

The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices

Mehdi Dehghan Faculty of Mathematics and Computer Sciences, Department of Applied Mathematics, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, IranCorrespondence[email protected]
&
Masoud Hajarian Faculty of Mathematics and Computer Sciences, Department of Applied Mathematics, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran; Faculty of Mathematical Sciences, Department of Mathematics, Shahid Beheshti University, Evin, Tehran 19839, Iran
Pages 1580-1590 | Received 30 Jan 2010, Accepted 13 Oct 2010, Published online: 14 Feb 2011

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Ai-Guo Wu, Ying Zhang & Tong-Yang Jiang. (2019) Iterative algorithms for discrete periodic Riccati matrix equations. International Journal of Systems Science 50:11, pages 2102-2112.
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Chang-Qing Lv & Chang-Feng Ma. (2019) The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix. International Journal of Computer Mathematics 96:8, pages 1576-1594.
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Masoud Hajarian. (2015) Finite algorithms for solving the coupled Sylvester-conjugate matrix equations over reflexive and Hermitian reflexive matrices. International Journal of Systems Science 46:3, pages 488-502.
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Jing Chen & Hongfen Zou. (2014) An interesting method for the exponentials for some special matrices. Systems Science & Control Engineering 2:1, pages 2-6.
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Wenli Wang & Caiqin Song. (2023) A NOVEL ITERATIVE METHOD FOR SOLVING THE COUPLED SYLVESTER-CONJUGATE MATRIX EQUATIONS AND ITS APPLICATION IN ANTILINEAR SYSTEM. Journal of Applied Analysis & Computation 13:1, pages 249-274.
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Wenli Wang, Caiqin Song & Shipu Ji. (2021) Iterative solution to a class of complex matrix equations and its application in time-varying linear system. Journal of Applied Mathematics and Computing 67:1-2, pages 317-341.
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Caiqin Song. (2020) Iterative method to the coupled operator matrix equations with sub-matrix constraint and its application in control. Transactions of the Institute of Measurement and Control, pages 014233122094756.
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Changfeng Ma & Tongxin Yan. (2020) AN ITERATIVE ALGORITHM FOR SOLVING A CLASS OF GENERALIZED COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS OVER BISYMMETRIC OR SKEW-ANTI-SYMMETRIC MATRICES. Journal of Applied Analysis & Computation 10:4, pages 1282-1310.
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Baohua Huang & Changfeng Ma. (2018) The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint. Journal of Global Optimization 73:1, pages 193-221.
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Ivan Kyrchei. (2018) Cramer’s Rules for Sylvester Quaternion Matrix Equation and Its Special Cases. Advances in Applied Clifford Algebras 28:5.
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Jingjing Hu & Changfeng Ma. (2018) Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations. Applied Mathematics and Computation 334, pages 174-191.
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Baohua Huang & Changfeng Ma. (2017) An iterative algorithm for the least Frobenius norm Hermitian and generalized skew Hamiltonian solutions of the generalized coupled Sylvester-conjugate matrix equations. Numerical Algorithms 78:4, pages 1271-1301.
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Xingping Sheng. (2018) A relaxed gradient based algorithm for solving generalized coupled Sylvester matrix equations. Journal of the Franklin Institute 355:10, pages 4282-4297.
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Baohua Huang & Changfeng Ma. (2018) An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations. Applied Mathematics and Computation 328, pages 58-74.
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Basem I. Selim, Lei Du & Bo Yu. (2018) The GPBiCOR Method for Solving the General Matrix Equation and the General Discrete-Time Periodic Matrix Equations. IEEE Access 6, pages 68649-68674.
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Chang-Qing Lv & Chang-Feng Ma. (2018) BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix. Computers & Mathematics with Applications 75:1, pages 70-88.
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Guang-Jing Song & Shaowen Yu. (2017) The Solution of a Generalized Sylvester Quaternion Matrix Equation and Its Application. Advances in Applied Clifford Algebras 27:3, pages 2473-2492.
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Bao-Hua Huang & Chang-Feng Ma. (2017) On the least squares generalized Hamiltonian solution of generalized coupled Sylvester-conjugate matrix equations. Computers & Mathematics with Applications 74:3, pages 532-555.
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Jing-Jing Hu & Chang-Feng Ma. (2017) Minimum-norm Hamiltonian solutions of a class of generalized Sylvester-conjugate matrix equations. Computers & Mathematics with Applications 73:5, pages 747-764.
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Peng Wang, Shifang Yuan & Xiangyun Xie. (2016) Least-squares Hermitian problem of complex matrix equation ( A X B , C X D ) = ( E , F ) $(AXB,CXD)=(E,F)$. Journal of Inequalities and Applications 2016:1.
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? ?. (2016) Least Squares Hermitian Solution of Complex Matrix Equation <i>AXB</i> = <i>C</i>. Pure Mathematics 06:01, pages 42-49.
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Na Huang & Chang-Feng Ma. (2016) Modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations. Applied Mathematical Modelling 40:2, pages 1260-1275.
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Ya-Jun Xie & Chang-Feng Ma. (2015) The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations. Applied Mathematics and Computation 265, pages 68-78.
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Guang-Ren Duan. 2015. Generalized Sylvester Equations. Generalized Sylvester Equations 341 374 .
Shifang Yuan & Anping Liao. (2014) Least squares Hermitian solution of the complex matrix equation AXB+CXD=E with the least norm. Journal of the Franklin Institute 351:11, pages 4978-4997.
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Fatemeh Panjeh Ali Beik. (2014) A modified iterative algorithm for the (Hermitian) reflexive solution of the generalized Sylvester matrix equation. Transactions of the Institute of Measurement and Control 36:6, pages 815-827.
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Yajun Xie, Na Huang & Changfeng Ma. (2014) Iterative method to solve the generalized coupled Sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix. Computers & Mathematics with Applications 67:11, pages 2071-2084.
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Masoud Hajarian. (2014) Convergence of ADGI methods for solving systems of linear matrix equations. Engineering Computations 31:4, pages 681-690.
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Na Huang & Changfeng Ma. (2014) The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations. Computers & Mathematics with Applications 67:8, pages 1545-1558.
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Mehdi Dehghan & Masoud Hajarian. (2012) Solving the system of generalized Sylvester matrix equations over the generalized centro-symmetric matrices. Journal of Vibration and Control 20:6, pages 838-846.
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Fatemeh Panjeh Ali Beik, Davod Khojasteh Salkuyeh & Mahmoud Mohseni Moghadam. (2013) Gradient-based iterative algorithm for solving the generalized coupled Sylvester-transpose and conjugate matrix equations over reflexive (anti-reflexive) matrices. Transactions of the Institute of Measurement and Control 36:1, pages 99-110.
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Dongqing Wang, Feng Ding & Liu Ximei. (2013) Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dynamics 75:1-2, pages 49-61.
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Mehdi Dehghan & Masoud Hajarian. (2012) Construction of an iterative method for solving generalized coupled Sylvester matrix equations. Transactions of the Institute of Measurement and Control 35:8, pages 961-970.
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Peipei Hu, Feng Ding & Jie Sheng. (2013) Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle. Journal of the Franklin Institute 350:10, pages 3248-3259.
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Zhuohua Peng & Huimin Xin. (2013) The reflexive least squares solutions of the general coupled matrix equations with a submatrix constraint. Applied Mathematics and Computation 225, pages 425-445.
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Masoud Hajarian. (2014) Efficient Iterative Solutions to General Coupled Matrix Equations. International Journal of Automation and Computing 10:5, pages 481-486.
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Mehdi Dehghan & Masoud Hajarian. (2012) On the generalized reflexive and anti-reflexive solutions to a system of matrix equations. Linear Algebra and its Applications 437:11, pages 2793-2812.
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Mehdi Dehghan & Masoud Hajarian. (2012) Solving coupled matrix equations over generalized bisymmetric matrices. International Journal of Control, Automation and Systems 10:5, pages 905-912.
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