Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices

Abstract

The Toeplitz Procrustes problems are the least squares problems for the matrix equation $AX=B$ over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible.