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Finite iterative method for solving coupled Sylvester-transpose matrix equations
Authors:Caiqin Song  Jun-e Feng  Xiaodong Wang  Jianli Zhao
Institution:1. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, 266590, P.R. China
2. School of Mathematics, Shandong University, Jinan, 250100, P.R. China
3. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, P.R. China
4. College of Mathematics Science, Liaocheng University, Liaocheng, 252059, P.R. China
Abstract:This paper is concerned with solutions to the so-called coupled Sylvester-transpose matrix equations, which include the generalized Sylvester matrix equation and Lyapunov matrix equation as special cases. By extending the idea of conjugate gradient method, an iterative algorithm is constructed to solve this kind of coupled matrix equations. When the considered matrix equations are consistent, for any initial matrix group, a solution group can be obtained within finite iteration steps in the absence of roundoff errors. The least Frobenius norm solution group of the coupled Sylvester-transpose matrix equations can be derived when a suitable initial matrix group is chosen. By applying the proposed algorithm, the optimal approximation solution group to a given matrix group can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, a numerical example is given to illustrate that the algorithm is effective.
Keywords:
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