Year: 2004
Author: Zhenyun Peng, Xiyan Hu, Lei Zhang
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 6 : pp. 873–880
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10291
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 6 : pp. 873–880
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Bisymmetric matrix Matrix equation Matrix nearness problem Kronecker product Frobenius norm Moore-Penrose generalized inverse.