| 一类四元数矩阵方程的循环解及其最佳逼近 |
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| 引用本文： | 黄敬频,谭云龙,许克佶. 一类四元数矩阵方程的循环解及其最佳逼近[J]. 数学杂志, 2014, 34(2): 353-359 |
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| 作者姓名： | 黄敬频 谭云龙 许克佶 |
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| 作者单位： | 广西民族大学理学院; |
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| 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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| 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.
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| 关 键 词： | 四元数体 循环矩阵 最小二乘 最佳逼近 |
| 收稿时间： | 2013-03-05 |
| 修稿时间： | 2013-05-08 |
CIRCULANT MATRIX SOLUTION TO A CLASS OF QUATERNION MATRIX EQUATION AND ITS OPTIMAL APPROXIMATION |
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| HUANG Jing-pin,TAN Yun-long and XU Ke-ji. CIRCULANT MATRIX SOLUTION TO A CLASS OF QUATERNION MATRIX EQUATION AND ITS OPTIMAL APPROXIMATION[J]. Journal of Mathematics, 2014, 34(2): 353-359 |
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| Authors: | HUANG Jing-pin TAN Yun-long XU Ke-ji |
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| Affiliation: | College of Science, Guangxi University for Nationalities, Nanning 530006, China,College of Science, Guangxi University for Nationalities, Nanning 530006, China and College of Science, Guangxi University for Nationalities, Nanning 530006, China |
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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. |
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| Keywords: | quaternion field circulant matrix least square optimal approximation |
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