An Iterative Method For The Generalized Bisymmetric Solution Of The Linear Matrix Equation AXB=C

The study of matrix equations is a very important branch of the matrix theory, which has been widely used in mathematics and other sciences. So various forms of solving linear equations become one of the most active areas of computational mathematics. The main issue of this paper is the generalized bisymmetric solution of linear matrix equation. The important role of symmetric solutions, symmetric center solutions, bisymmetric solutions and image-symmetric solutions of linear ma-trix equations in electronic networks, dynamic programming, stochastic processes, control theory, statistics and so on caused many scholars to study the issue. Mean-while their study has got some achievement.The main problem of this study is the numerical solving method of the gen-eralized bisymmetric solution of linear matrix equation AXB=C. This problem is equivalent to the minimum remaining issue:min‖AXB-C‖. We give a new iterative algorithm for solving this problem. we prove the convergence of the new algorithm. The numerical example illustrate the efficiency of the algorithm.