An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation AXB=C

Authors:
Guang-Xin Huang;Feng Yin;Ke Guo
Affiliations:
College of Information and Management, Chengdu University of Technology, Chengdu 610059, PR China;Department of Mathematics, Sichuan University of Science and Engineering, Zigong 643000, PR China;College of Information and Management, Chengdu University of Technology, Chengdu 610059, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, an iterative method is constructed to solve the linear matrix equation AXB=C over skew-symmetric matrix X. By the iterative method, the solvability of the equation AXB=C over skew-symmetric matrix can be determined automatically. When the equation AXB=C is consistent over skew-symmetric matrix X, for any skew-symmetric initial iterative matrix X"1, the skew-symmetric solution can be obtained within finite iterative steps in the absence of roundoff errors. The unique least-norm skew-symmetric iterative solution of AXB=C can be derived when an appropriate initial iterative matrix is chosen. A sufficient and necessary condition for whether the equation AXB=C is inconsistent is given. Furthermore, the optimal approximate solution of AXB=C for a given matrix X"0 can be derived by finding the least-norm skew-symmetric solution of a new corresponding matrix equation AX@?B=C@?. Finally, several numerical examples are given to illustrate that our iterative method is effective.