An iterative method for the skewsymmetric solution and the optimal approximate solution of the matrix equation AXB=C
Abstract
In this paper, an iterative method is constructed to solve the linear matrix equation AXB=C over skewsymmetric matrix X. By the iterative method, the solvability of the equation AXB=C over skewsymmetric matrix can be determined automatically. When the equation AXB=C is consistent over skewsymmetric matrix X, for any skewsymmetric initial iterative matrix X1, the skewsymmetric solution can be obtained within finite iterative steps in the absence of roundoff errors. The unique leastnorm skewsymmetric 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 X0 can be derived by finding the leastnorm skewsymmetric solution of a new corresponding matrix equation E Finally, several numerical examples are given to illustrate that our iterative method is effective.
 Publication:

Journal of Computational and Applied Mathematics
 Pub Date:
 March 2008
 Bibcode:
 2008JCoAM.212..231H
 Keywords:

 Iterative method;
 Skewsymmetric solution;
 Leastnorm skewsymmetric solution;
 Optimal approximate solution