| 求解最近保体矩阵问题的若干研究 |
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| 引用本文： | 沐建飞,黄建国. 求解最近保体矩阵问题的若干研究[J]. 东南大学学报, 2005, 21(1): 119-122 |
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| 作者姓名： | 沐建飞 黄建国 |
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| 作者单位： | 上海交通大学数学系，上海200240 |
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| 摘 要： | 研究了求解给定矩阵的最近保体矩阵问题，首先导出该问题解所必须满足的一个矩阵方程，然后用奇异值分解方法求解该矩阵方程；并获得了该问题解的其他更进一步的刻画条件，利用这些结果建立了一个求解算法，并通过数值算例说明了该算法的有效性。
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| 关 键 词： | 保体矩阵 矩阵拟合问题 奇异值分解 |
Some studies on finding the nearest volume-preserving matrix |
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| Mu Jianfei,Huang Jianguo. Some studies on finding the nearest volume-preserving matrix[J]. Journal of Southeast University(English Edition), 2005, 21(1): 119-122 |
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| Authors: | Mu Jianfei Huang Jianguo |
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| Abstract: | Finding the nearest volume-preserving matrix for a given matrix is studied.A matrix equation is first obtained,which is a necessary condition for the solution to the problem.Then the equation is solved by the singular value decomposition method.Some additional results are also provided to further characterize the solution.Using these results,a numerical algorithm is introduced and a numerical test is given to illustrate the effectiveness of the algorithm. |
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| Keywords: | volume-preserving matrix matrix nearness problem singular value decomposition |
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