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给出了非负矩阵Perron根的一系列优化上界,即通过相似对角变换与Gerschgorin定理较好的估计了Perron根的上界,并且通过例子来说明这种方法的有效性. 相似文献
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对于非负矩阵A,主要讨论其谱半径即Perron根的估计.这里提出了一种利用非负矩阵的Perron补矩阵与Perron根关系来估计其Perron根上下界的新方法,并且给出例子来说明这种方法的有效性. 相似文献
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关于非负矩阵Perron特征值的上、下界 总被引:3,自引:0,他引:3
陈恒新 《应用数学与计算数学学报》2007,21(1):1-8
本文通过构造一可逆矩阵,对一类非负矩阵A进行若干次简单的相似变换,便可同时得到矩阵A之Perron特征值的较好的上、下界. 相似文献
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给出了非负矩阵Perron根的一系列优化上界,即通过相似对角变换与Gerschgorin定理较好的估计了Perron根的上界,并且通过例子来说明这种方法的有效性. 相似文献
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Estimate bounds for the Perron root of a nonnegative matrix are important in theory of nonnegative matrices. It is more practical when the bounds are expressed as an easily calculated function in elements of matrices. For the Perron root of nonnegative irreducible matrices, three sequences of lower bounds are presented by means of constructing shifted matrices, whose convergence is studied. The comparisons of the sequences with known ones are supplemented with a numerical example. 相似文献
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非负矩阵Perron根的上下界 总被引:9,自引:0,他引:9
1.引言 本文主要讨论非负矩阵,我们将用B≥0和B>0分别表示矩阵B是非负的和正的,也就是B的每一个元素是非负的和B的每一个元素是正的.用p(B)表示方阵B的谱半径,当B≥0时,p(B)也就是B的perron根. 设(n)={1,2,…,n},A=(ai,j)是n×n非负矩阵,我们称 相似文献
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文章针对特殊的非负矩阵,应月简单的相似变换,使矩阵保持非负性且最大行和减小,从而得到行和为正非负矩阵Perron根的新上界. 相似文献
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A. Melman 《Linear and Multilinear Algebra》2013,61(2):171-181
We derive upper and lower bounds for the Perron root of a nonnegative matrix by using generalized Gershgorin inclusion regions. Our bounds seem particularly effective for certain sparse matrices. 相似文献
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Carl D. Meyer 《Linear and Multilinear Algebra》2013,61(7):1332-1336
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A modified algorithm for the Perron root of a nonnegative matrix 总被引:1,自引:0,他引:1
Chengming Wen Ting-Zhu Huang 《Applied mathematics and computation》2011,217(9):4453-4458
An algorithm of diagonal transformation for the Perron root of nonnegative matrices is proposed by Duan and Zhang [F. Duan, K. Zhang, An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices, Appl. Math. Comput. 175 (2006) 762-772]. This method can be used for all nonnegative irreducible matrices. In this paper, an improved algorithm which is based on this method is proposed. The new algorithm inherits all the above-mentioned advantages of the original algorithm and has higher efficiency. It is testified by numerical testing that the efficiency of the new algorithm is improved greatly. 相似文献
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Guang-Xin Huang Feng Yin Ke Guo 《Journal of Computational and Applied Mathematics》2008,217(1):259-267
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In this paper, we obtain some new bounds for Perron root of a nonnegative matrix, which are expressed by easily calculated function in element of matrix. These new results generalize and improve the bounds of G. Frobenius [1] and H. Minc [2], and also extend the known results by Liu [6]. 相似文献