• 论文 •

### 多矩阵变量线性矩阵方程的广义自反解的迭代算法

1. 西北工业大学应用数学系, 西安 710072
• 收稿日期:2011-11-17 出版日期:2013-03-15 发布日期:2013-03-12
• 基金资助:

国家自然科学基金(11071196).

Wang Jiao, Zhang Kaiyuan, Li Shulian. AN ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE SOLUTION OF THE MULTI-MATRIX-VARIABLE LINEAR MATRIX EQUATION[J]. Journal of Numerical Methods and Computer Applications, 2013, 34(1): 9-19.

### AN ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE SOLUTION OF THE MULTI-MATRIX-VARIABLE LINEAR MATRIX EQUATION

Wang Jiao, Zhang Kaiyuan, Li Shulian

1. Dept. of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
• Received:2011-11-17 Online:2013-03-15 Published:2013-03-12

Based on the method of the modified conjugate gradient to the linear matrix equation over constrained matrices, and by modifying the construction of some matrices, an iterative algorithm is presented to find the generalized reflexive solution of the matrix equation which is a special type with several matrix variables. The convergence of the iterative algorithm is proved. And the problem of the optimal approximation to the given matrix is solved in the generalized reflexive solution set of this matrix equation. When this matrix equation is consistent, its generalized reflexive solution can be obtained within finite iterative steps. And its least-norm generalized reflexive solution can be got by choosing the special initial matrices. The numerical example shows that the iterative algorithm is quite efficient.

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