| 广义对角占优矩阵的新判据及其在神经网络系统中的应用 |
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| 引用本文： | 王峰.广义对角占优矩阵的新判据及其在神经网络系统中的应用[J].贵州大学学报(自然科学版),2012,29(5):1-4. |
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| 作者姓名： | 王峰 |
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| 作者单位： | 菏泽学院数学系,山东 菏泽 274015;云南大学数学与统计学院,云南 昆明 6500911 |
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| 基金项目： | 基金项目：国家自然科学基金项目（10961027,71161020）;山东省教育科学重点课题项目（2011GG049） |
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| 摘 要： | 广义对角占优矩阵在矩阵分析和数值代数的研究中具有重要作用,但在实用中要判别广义对角占优矩阵是十分困难的。本文通过对矩阵行标作划分的方法,给出了判定广义对角占优矩阵的一组新条件,改进了近期的相关结果,并给出其在神经网络系统中的应用,相应数值例子说明了结果的有效性。
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| 关 键 词： | 广义对角占优矩阵 神经网络系统 对角占优性 不可约 非零元素链 |
New Criteria for Generalized Diagonally Dominant Matrices and Its Application on Neural Network System |
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| WANG Feng.New Criteria for Generalized Diagonally Dominant Matrices and Its Application on Neural Network System[J].Journal of Guizhou University(Natural Science),2012,29(5):1-4. |
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| Authors: | WANG Feng |
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| Institution: | WANG Feng ( 1. Department of Mathematics, Heze University, Heze 274015, China;2. School of Mathematics and Statistics, Yunnan University, Kunming 650091, China) |
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| Abstract: | Generalized diagonally dominant matrices play a very important role in the research of matrix analysis and numerical algebra. But it is difficult to determine a generalized diagonally dominant matrix in practice. In this paper, some sufficient conditions for generalized diagonally dominant matrices were obtained according to the partition of the row indices, some related results were improved, and its application on neural network system was given. Advantages of results obtained were illustrated by a numerical example. |
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| Keywords: | generalized diagonally dominant matrices neural network system diagonally dominant irreducible nonzero elements chain |
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