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

摘要

In this paper, an iterative method is constructed to solve the linear matrix equation over skew-symmetric matrix X. By the iterative method, the solvability of the equation over skew-symmetric matrix can be determined automatically. When the equation is consistent over skew-symmetric matrix X, for any skew-symmetric initial iterative matrix , 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 can be derived when an appropriate initial iterative matrix is chosen. A sufficient and necessary condition for whether the equation is inconsistent is given. Furthermore, the optimal approximate solution of for a given matrix can be derived by finding the least-norm skew-symmetric solution of a new corresponding matrix equation . Finally, several numerical examples are given to illustrate that our iterative method is effective.