The reflexive least squares solutions of the matrix equation A_1X_1B_1+A_2X_2B_2+\cdots +A_lX_lB_l=Cwith a submatrix constraint |
| |
Authors: | Zhuohua Peng |
| |
Institution: | 1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, 411201, People’s Republic of China
|
| |
Abstract: | In this paper, an efficient algorithm is presented for minimizing $\|A_1X_1B_1 + A_2X_2B_2+\cdots +A_lX_lB_l-C\|$ where $\|\cdot \|$ is the Frobenius norm, $X_i\in R^{n_i \times n_i}(i=1,2,\cdots ,l)$ is a reflexive matrix with a specified central principal submatrix $x_{ij}]_{r\leq i,j\leq n_i-r}$ . The algorithm produces suitable $X_1,X_2,\cdots ,X_l]$ such that $\|A_1X_1B_1+A_2X_2B_2+\cdots +A_lX_lB_l-C\|=\min $ within finite iteration steps in the absence of roundoff errors. We show that the algorithm is stable any case. The algorithm requires little storage capacity. Given numerical examples show that the algorithm is efficient. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|