TY - JOUR
T1 - The Nearest Bisymmetric Solutions of Linear Matrix Equations
AU - Peng , Zhenyun
AU - Hu , Xiyan
AU - Zhang , Lei
JO - Journal of Computational Mathematics
VL - 6
SP - 873
EP - 880
PY - 2004
DA - 2004/12
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10291.html
KW - Bisymmetric matrix, Matrix equation, Matrix nearness problem, Kronecker product, Frobenius norm, Moore-Penrose generalized inverse.
AB - <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>