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Linear and Multilinear Algebra Volume 59, 2011 - Issue 11
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Original Articles

On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations

Mehdi Dehghan Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424 Hafez Avenue, Tehran 15914, IranCorrespondence[email protected]
&
Masoud Hajarian Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424 Hafez Avenue, Tehran 15914, Iran
Pages 1281-1309 | Received 20 Nov 2008, Accepted 03 Sep 2010, Published online: 20 Apr 2011

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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. (2018) Convergence properties of BCR method for generalized Sylvester matrix equation over generalized reflexive and anti-reflexive matrices. Linear and Multilinear Algebra 66:10, pages 1975-1990.
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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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Di Gan, Guo-Feng Zhang & Zhao-Zheng Liang. (2023) Preconditioning techniques of all-at-once systems for multi-term time-fractional diffusion equations. Numerical Algorithms.
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Fengxia Zhang, Ying Li & Jianli Zhao. (2022) The semi-tensor product method for special least squares solutions of the complex generalized Sylvester matrix equation. AIMS Mathematics 8:3, pages 5200-5215.
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Mohamed A. Ramadan, Naglaa M. El–shazly & Basem I. Selim. (2019) Iterative algorithm for the reflexive solutions of the generalized Sylvester matrix equation. Journal of the Egyptian Mathematical Society 27:1.
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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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Fengxia Zhang, Musheng Wei, Ying Li & Jianli Zhao. (2018) An efficient method for special least squares solution of the complex matrix equation . Computers & Mathematics with Applications 76:8, pages 2001-2010.
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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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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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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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Xindong Zhang & Xinlong Feng. (2017) The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation. International Journal of Nonlinear Sciences and Numerical Simulation 18:5, pages 293-301.
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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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Masoud Hajarian. (2016) Symmetric solutions of the coupled generalized Sylvester matrix equations via BCR algorithm. Journal of the Franklin Institute 353:13, pages 3233-3248.
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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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Masoud Hajarian. (2015) Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester matrix equations. Applied Mathematical Modelling 39:19, pages 6073-6084.
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Masoud Hajarian. (2014) Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations. Computational and Applied Mathematics 34:2, pages 755-771.
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Guang-Ren Duan. 2015. Generalized Sylvester Equations. Generalized Sylvester Equations 341 374 .
Masoud Hajarian. (2015) Matrix GPBiCG algorithms for solving the general coupled matrix equations. IET Control Theory & Applications 9:1, pages 74-81.
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Masoud Hajarian. (2014) Extending the GPBiCG algorithm for solving the generalized Sylvester-transpose matrix equation. International Journal of Control, Automation and Systems 12:6, pages 1362-1365.
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Masoud Hajarian. (2013) Developing the CGLS algorithm for the least squares solutions of the general coupled matrix equations. Mathematical Methods in the Applied Sciences 37:17, pages 2782-2798.
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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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Masoud Hajarian. (2013) Extending LSQR methods to solve the generalized Sylvester‐transpose and periodic Sylvester matrix equations. Mathematical Methods in the Applied Sciences 37:13, pages 2017-2028.
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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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Mehdi Dehghan & Masoud Hajarian. (2012) Modied AOR iterative methods to solve linear systems. Journal of Vibration and Control 20:5, pages 661-669.
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Masoud Hajarian. (2013) A gradient-based iterative algorithm for generalized coupled Sylvester matrix equations over generalized centro-symmetric matrices. Transactions of the Institute of Measurement and Control 36:2, pages 252-259.
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Masoud Hajarian. (2015) Developing Bi-CG and Bi-CR Methods to Solve Generalized Sylvester-transpose Matrix Equations. International Journal of Automation and Computing 11:1, pages 25-29.
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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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Masoud Hajarian. (2013) Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations. Journal of the Franklin Institute 350:10, pages 3328-3341.
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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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Masoud Hajarian. (2013) Matrix form of the Bi‐CGSTAB method for solving the coupled Sylvester matrix equations. IET Control Theory & Applications 7:14, pages 1828-1833.
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Qing-Wen Wang & Juan Yu. (2013) On the generalized bi (skew-) symmetric solutions of a linear matrix equation and its procrust problems. Applied Mathematics and Computation 219:19, pages 9872-9884.
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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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