| 四元数体上线性方程组的加正定权极小范数最小二乘解 |
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| 引用本文： | 徐清舟,汪国军.四元数体上线性方程组的加正定权极小范数最小二乘解[J].河南师范大学学报(自然科学版),2005,33(2):19-22. |
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| 作者姓名： | 徐清舟 汪国军 |
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| 作者单位： | 1. 许昌学院,数学系,河南,许昌,461000
2. 浙江大学,数学系,杭州,310028 |
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| 基金项目： | 国家自然科学基金资助项目(60364001) |
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| 摘 要： | 讨论了四元数体上右线性方程组的加正定权的极小范数解、最小二乘解和极小范数最小二乘解.得到类似于复数域上同类问题的若干结果.
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| 关 键 词： | 四元数体 加权广义逆 极小范数解 最小二乘解 |
| 文章编号： | 1000-2367(2005)02-0019-04 |
| 修稿时间： | 2004年9月21日 |
The Minimal Norm and the Least Square Solution of a System of Linear Equations over the Quaternion Field |
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| XU Qing-zhou,WANG Guo-jun.The Minimal Norm and the Least Square Solution of a System of Linear Equations over the Quaternion Field[J].Journal of Henan Normal University(Natural Science),2005,33(2):19-22. |
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| Authors: | XU Qing-zhou WANG Guo-jun |
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| Institution: | XU Qing-zhou~1,WANG Guo-jun~2 |
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| Abstract: | In this paper,for a right system of linear equations Ax=b over the quaternion field,we discuss, under the condition of a positive definite weight,the solutions with minimal N-norms, the M-least square solutions and in particular, the M-least square solutions with minimal N-norms. Some main results are obtained, which can be considered as the correspondent conclusions for the similar questions in the case of the complex field. |
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| Keywords: | quaternion field weighted generalized inverse solution with minimal norm least square solution |
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