An iteration method for the symmetric solutions to the matrix equation AT XA=B

摘要

In this paper, a class of iterative method for the symmetric solution to the matrix equation AT XA=B is constructed. By this iteration method, the least-norm symmetric solution for the matrix equation can be obtained when the problem is consistent. The related optimal approximation solution is also obtained by this iteration method. The analysis for the convergence of the method shows that the convergence rates can be improved by preconditioned methods.