University of Guilan
Journal of Mathematical Modeling
2345-394X
2
2
2015
05
01
Global least squares solution of matrix equation $\sum_{j=1}^s A_jX_jB_j = E$
170
186
109
EN
Saeed
Karimi
Journal Article
2015
05
21
In this paper, an iterative method is proposed for solving matrix equation $\sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are definned. It is proved that the new iterative method obtains the least norm solution of the mentioned matrix equation within finite iteration steps in the exact arithmetic, when the above matrix equation is consistent. Moreover, the optimal approximate solution $(X_1^* ,X_2^* ,\ldots,X_s^*)$ to a given multiple matrices $( \bar{X}_1, \bar{X}_2,\ldots,\bar{X}_s)$ can be derived by finding the least norm solution of a new matrix equation. Finally, some numerical experiments are given to illustrate the efficiency of the new method.
https://jmm.guilan.ac.ir/article_109_cfc63352c7ee49587886dd418b5004f8.pdf