| 四元数体上一类矩阵方程的极小范数最小二乘解 |
| |
| 引用本文： | 邓勇,黄敬频,杜刚.四元数体上一类矩阵方程的极小范数最小二乘解[J].纯粹数学与应用数学,2010,26(2):191-192,230. |
| |
| 作者姓名： | 邓勇 黄敬频 杜刚 |
| |
| 作者单位： | 喀什师范学院数学系,新疆,喀什,844007;广西民族大学数计学院,广西,南宁,530006 |
| |
| 基金项目： | 新疆维吾尔自治区高校科研计划重点项目 |
| |
| 摘 要： | 借助于四元数体上自共轭矩阵的奇异值分解,给出了四元数矩阵方程AX＋XB＋CXD=F的极小范数最小二乘解.同时,在有解的条件下给出了Hermite最小二乘解及其通解的表达形式.
|
| 关 键 词： | 四元数体 矩阵方程 最小二乘解 |
The minimal norm and least square solution to a class of matrix equations in the quaternion field |
| |
| DENG Yong,HUANG Jing-pin,DU Gang.The minimal norm and least square solution to a class of matrix equations in the quaternion field[J].Pure and Applied Mathematics,2010,26(2):191-192,230. |
| |
| Authors: | DENG Yong HUANG Jing-pin DU Gang |
| |
| Institution: | DENG Yong1,HUANG Jing-pin2,DU Gang1(1.Department of Mathematics of Kashi Teachers College,Kashi 844007,China,2.College of Computer , Information Science,Guangxi University for Nationalities,Nanning 530006,China) |
| |
| Abstract: | By using the singular value decomposition of self-conjugate matrices in the quaternion field,we obtain the least square solutions with minimal norms to AX+XB+CXD=F.At the same time,we gave exact form of the least square solution of Hermite,if it has solutions. |
| |
| Keywords: | quaternion field matrix equation least square solution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
