| 逆M矩阵模型的完备及其算法设计 |
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| 引用本文： | 刘德友,姚惠萍,刘志华.逆M矩阵模型的完备及其算法设计[J].高等学校计算数学学报,2003,25(3):276-288. |
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| 作者姓名： | 刘德友 姚惠萍 刘志华 |
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| 作者单位： | 燕山大学理学院,秦皇岛,066004 |
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| 基金项目： | 河北省博士基金(2002131) |
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| 摘 要： | 1 引 言 M矩阵是具有非负对角元和非正非对角元且其逆是非负矩阵的一类矩阵.逆M矩阵即逆为M矩阵的一类非负矩阵.逆M矩阵在物理学,生物学,控制理论,神经网络方面有着重要的应用.所以对逆M矩阵的研究一直在持续不断的进行.一个“部分矩阵”是指在一个矩阵中,一些元素已经给定了,而另一些元素待定的矩阵.而一个矩阵的完
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| 关 键 词： | 逆M矩阵 模型 算法 有向图 回路 完备 半团图 |
| 修稿时间： | 2002年7月8日 |
COMPLETIONS OF INVERSE MATRIX PATTERNS AND ALGORITHM DESIGN |
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| Liu Deyou Yao Huiping Liu Zhihua.COMPLETIONS OF INVERSE MATRIX PATTERNS AND ALGORITHM DESIGN[J].Numerical Mathematics A Journal of Chinese Universities,2003,25(3):276-288. |
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| Authors: | Liu Deyou Yao Huiping Liu Zhihua |
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| Abstract: | In this paper, problems for any nonnegative partial matrix pattern of any order to have inverse M-matrix completion are discussed. The partial matrices are not limited within the condition of position symmetry and the matrix is unnecessarily symmetric. And a graph-theoretic completion result is given for the inverse M-matrix problem. The graph due to the pattern can be direction cycle, semi-cycle, hypo-cycle and semi-block clique graph. The algorithm which can be used effectively to get the completion is also presented. |
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| Keywords: | inverse M-matrix partial matrix completion pattern semi-block clique graph hypo-cycle semi-cycle |
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