Volume 16, Issue 3
Least-Squares Solutions of the Matrix Equation ATXA=B Over Bisymmetric Matrices and its Optimal Approximation

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 215-225

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• Abstract

A real $n\times n$ symmetric matrix $X=(x_{ij})_{n \times n}$ is called a bisymmetric matrix if $x_{ij}=x_{n+1-j, n+1-i}$. Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation $A^{T}XA=B$ over bisymmetric matrices is proposed. The expression of the least-squares solutions is given. Moreover, in the corresponding solution set, the optimal approximate solution to a given matrix is also derived. A numerical algorithm for finding the optimal approximate solution is also described.

• History

Published online: 2007-08

• Keywords