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| 摘要: |
| 本文研究了四元数体上矩阵方程XB = C 的循环解及其最佳逼近问题. 利用循环矩阵的结构表示式, 以及四元数矩阵的复分解, 得到了方程XB = C 的循环解存在条件及其通解形式; 在循环矩阵约束条件下, 给出了该方程的最小二乘解集合; 与此同时, 在最小二乘解集合中, 获得与给定四元数循环矩阵的最佳逼近解. 推广了约束矩阵方程的数值求解范围. 数值算例验证了本文算法的可行性. |
| 关键词: 四元数体 循环矩阵 最小二乘 最佳逼近 |
| DOI： |
| 分类号:O241.6 |
| 基金项目:广西高校科研项目(2013YB076);广西民族大学研究生教育创新项目(gxun-chx2012099) |
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| CIRCULANT MATRIX SOLUTION TO A CLASS OF QUATERNION MATRIX EQUATION AND ITS OPTIMAL APPROXIMATION |
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HUANG Jing-pin,TAN Yun-long,XU Ke-ji
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| Abstract: |
| This paper is focused on the problem of the circulant matrix solution of quaternion matrix equation XB = C and its optimal approximation. By using the structural formulas of a circulant matrix and complex representation of a quaternion matrix, the existence conditions of circulant matrix solution and its general solutions of the equation XB = C are obtained, and the set of the least-square solution under constrain condition with circulant matrix is obtained. Meanwhile, in the above set of the least-square solution, the optimal approximation solution giving the quaternion circulant matrix is derived, which extend the range to solve the constrained matrix equation. A numerical example shows feasibility of the method. |
| Key words: quaternion field circulant matrix least square optimal approximation |
