The Nearest Bisymmetric Solutions of Linear Matrix Equations

The Nearest Bisymmetric Solutions of Linear Matrix Equations

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.

Author Details

Zhenyun Peng

Xiyan Hu

Lei Zhang