The (M, N)-symmetric Procrustes problem

Abstract: An matrix A is said to be -symmetric if for given . In this paper, the following -symmetric Procrustes problem is studied. Find the -symmetric matrix A which minimizes the Frobenius norm of , where X and B are given rectangular matrices. We use Project Theorem, the singular-value decomposition and the generalized singular-value decomposition of matrices to analysis the problem and to derive a stable method for its solution. The related optimal approximation problem to a given matrix on the solution set is solved. Furthermore, the algorithm to compute the optimal approximate solution and the numerical experiment are given. [Copyright &y& Elsevier]