@Article{NM-16-215,
author = { Y. Y. Zhang and Y. Lei & A. P. Liao},
title = {Least-Squares Solutions of the Matrix Equation *A*^{T}XA=B Over Bisymmetric Matrices and its Optimal Approximation},
journal = {Numerical Mathematics, a Journal of Chinese Uniersities},
year = {2007},
volume = {16},
number = {3},
pages = {215--225},
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.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nm/8055.html}
}