|
| 摘要: |
| 本文研究了四元数体上Sylvester方程具有Toeplitz矩阵约束解及其最佳逼近问题.利用四元数矩阵的实分解和矩阵Kronecker积，获得四元数Sylvester方程AX-XB=C具有Toeplitz矩阵解的充要条件及其通解表达式.同时在Toeplitz解集合中，得到与预先给定的四元数Toeplitz矩阵有极小Frobenius范数的最佳逼近解. |
| 关键词: 四元数体 Sylvester方程 Toeplitz矩阵 最佳逼近 |
| DOI： |
| 分类号:O151.21 |
| 基金项目:国家自然科学基金项目（11661011）；广西民族大学研究生创新项目（gxun-chxzs2017142）. |
|
| TOEPLITZ SOLUTION OF SYLVESTER EQUATION AND ITS OPTIMAL APPROXIMATION OVER QUATERNION FIELD |
|
HUANG Jing-pin,LAN Jia-xin,MAO Li-ying,WANG Min
|
| Abstract: |
| In this paper, we study the Toeplitz matrix solution of Sylvester equation and its optimal approximation over quaternion field. By using the real representation of a quaternion matrix and Kronecker product of matrices, the necessary and sufficient condition for the existence of a Toeplitz matrix solution and the general solution of the quaternion Sylvester equation AX-XB=C are obtained. Meanwhile, in the Toeplitz solution set, the expression of the optimal approximation solution to the given quaternion Toeplitz matrix is derived. |
| Key words: quaternion field Sylvester equation Toeplitz matrix optimal approximation |
