| 四元数矩阵方程AX-YB=C的最佳逼近解 |
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| 引用本文： | 黄敬频. 四元数矩阵方程AX-YB=C的最佳逼近解[J]. 数学理论与应用, 2004, 24(2): 1-4 |
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| 作者姓名： | 黄敬频 |
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| 作者单位： | 广西民族学院数学与计算机科学系，南宁，530006 |
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| 基金项目： | 广西民族学院科研基金资助项目 (0 2 SJX0 0 0 8) |
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| 摘 要： | 本利用四元数矩阵的广义Frobenius范数建立一个关于四元数矩阵的实函数，并讨论了它的极值问题．然后在四元数矩阵方程AX-YB=C的解集合中导出了与给定矩阵的最佳逼近解的表达式．
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| 关 键 词： | 四元数矩阵 矩阵方程 广义Frobenius范数 实函数 最佳逼近 |
The Solution of the Quaternion Matrix Equation AX-YB=C and Its Optimal Approximation |
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| Huang Jingping. The Solution of the Quaternion Matrix Equation AX-YB=C and Its Optimal Approximation[J]. Mathematical Theory and Applications, 2004, 24(2): 1-4 |
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| Authors: | Huang Jingping |
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| Abstract: | By using generalized Frobenius norm of the quaternion matrices,a real-valued function are established for the quaternion matrices,and discusses minimal value problem on its.Based on this,in the solution set of the quaternion matrix equation AX-YB=C,the expression of the optimal approximation solution to given matrices is derived. |
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| Keywords: | quaternion matrix matrix equation generalized Frobenius norm optimal approximation |
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