@Article{JCM-22-6,
author = {Zhenyun, Peng and Xiyan, Hu and Zhang, Lei},
title = {The Nearest Bisymmetric Solutions of Linear Matrix Equations},
journal = {Journal of Computational Mathematics},
year = {2004},
volume = {22},
number = {6},
pages = {873--880},
abstract = {<p style="text-align: justify;">The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (I) $A_1X_1B_1+A_2X_2B_2+\cdots+A_kX_kB_k=D$, (II) $A_1XB_1+A_2XB_2+\cdots+A_kXB_k=D$ and (III) $(A_1XB_1, A_2XB_2, ··· , A_kXB_k) =
(D_1, D_2, ··· , D_k)$ are derived by using Kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given. Numerical methods and numerical experiments of finding the nearest solutions are also provided.</p>},
issn = {1991-7139},
doi = {https://doi.org/2004-JCM-10291},
url = {https://global-sci.com/article/85271/the-nearest-bisymmetric-solutions-of-linear-matrix-equations}
}