TY - JOUR
T1 - Least-Squares Solutions of the Matrix Equation <em>A<sup>T</sup>XA=B</em> Over Bisymmetric Matrices and its Optimal Approximation
AU -  Y. Y. Zhang, Y. Lei & A. P. Liao
JO - Numerical Mathematics, a Journal of Chinese Universities
VL - 3
SP - 215
EP - 225
PY - 2007
DA - 2007/08
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nm/8055.html
KW - 
AB - 
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.