一类四元数矩阵方程的循环解及其最佳逼近  

CIRCULANT MATRIX SOLUTION TO A CLASS OF QUATERNION MATRIX EQUATION AND ITS OPTIMAL APPROXIMATION

作　　者：黄敬频[1] 谭云龙[1] 许克佶 

机构地区：[1]广西民族大学理学院,广西南宁530006

出　　处：《数学杂志》2014年第2期353-359,共7页Journal of Mathematics

基　　金：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)

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.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.

关 键 词：四元数体 循环矩阵 最小二乘 最佳逼近 

分 类 号：O241.6[理学—计算数学]