矩阵约束下矩阵方程组的双对称最小二乘解

Abstract

Abstract:

The general coupled matrix equations $\100dpi \inline $\sum\limits_{j=1}^lA_{ij}X_jB_{ij}=C_i,\;\;i=1,2,\cdots,t$$ ,   have numerous applications in control and system theory.    In this paper, an algorithm is constructed   to solve the   general coupled matrix equations where   $\100dpi \inline $X_j\in R^{n_j\times n_j}\;(j=1,2,\cdots,l)$$ is a bisymmetric  matrix with a specified central  principal submatrix. The algorithm produces suitable
   $\100dpi \inline $[X_1,X_2,\cdots,X_l]$$ such that    $\100dpi \inline $\sum\limits_{i=1}^t\|\sum\limits_{j=1}^lA_{ij}X_jB_{ij}-C_i\|$$    is minimized within a finite iteration steps in the absence of roundoff errors.
The algorithm requires little storage capacity.    Numerical examples are given to show that the algorithm is efficient.

Key words: General coupled matrix equations , Central principal submatrix , Bisymmetric solution , Submatrix constraint , Least squares solution.

CLC Number:

65F10

PENG Zhuo-Hua. The Bisymmetric Least Squares Solutions of the General Coupled |Matrix Equations with A Submatrix Constraint[J].Acta mathematica scientia,Series A, 2015, 35(1): 131-150.

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The Bisymmetric Least Squares Solutions of the General Coupled |Matrix Equations with A Submatrix Constraint

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