共查询到20条相似文献,搜索用时 109 毫秒
1.
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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《数学的实践与认识》2015,(17)
给出了非负不可约矩阵Perron根的一些上下界估计,设A为任意非负不可约矩阵,ρ(A)为其Perron根,则ρ(A)≤max{D_k,(r_1+r_2+…r_k)/k}其中D_k为矩阵A所有k阶主子阵之列和最大值,r_1≥r_2≥…≥r_n为从大到小排序的行和,所得结果易于计算且较经典的Frobienus界值精确.同时也得到一个类似下界. 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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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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计算非负不可约矩阵Perron根的对角变换(英文) 总被引:1,自引:0,他引:1
计算非负矩阵Perron根一般通过矩阵的对角变换,但是有的时候是不可行的.本文为非负不可约矩阵的计算给了一列对角变换.此种变换对所有的非负不可约矩阵实用,并且方便计算,最后给出了数值例子. 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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钟琴 《数学的实践与认识》2010,40(19)
1989年Meyer为计算马尔可夫链的平稳分布向量构造了一个算法,首次提出非负不可约矩阵Perron余的概念.将非负不可约矩阵Perron余的概念推广到逆N_0-矩阵的Perron余,并给出关于N_0-矩阵和逆N_0-矩阵的相关不等式. 相似文献
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计算非负矩阵Perron根一般通过矩阵的对角变换,但是有的时候是不可行的.本文为非负不可约矩阵的计算给了一列对角变换.此种变换对所有的非负不可约矩阵实用,并且方便计算,最后给出了数值例子. 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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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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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
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The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property
implies known monotonicity properties and also the Chistyakov two-sided bounds for the Perron root of a block-partitioned
nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov’s theorem are
analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 13–29. 相似文献
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Lilia Yu. Kolotilina 《Numerical Algorithms》2006,42(3-4):247-280
Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed. 相似文献
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L. Yu. Kolotilina 《Journal of Mathematical Sciences》2008,150(2):1973-1981
The paper presents new two-sided bounds for the Perron root of a block-partitioned nonnegative matrix, improving Chistyakov’s
bounds. The equality cases are analyzed. As an application, new conditions sufficient for a complex matrix to be a nonsingular
H-matrix are obtained. Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 103–118. 相似文献
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L. Yu. Kolotilina 《Journal of Mathematical Sciences》2004,121(4):2481-2507
In this paper, bounds and inequalities for the Perron root of a nonnegative matrix, extending and complementing the classical theorems of Frobenius and Ostrowski in terms of (deleted) row and column sums, are presented. All the results are derived by using the same approach, based on the monotonicity property of the Perron root. Bibliography: 12 titles. 相似文献
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L. Yu. Kolotilina 《Journal of Mathematical Sciences》2006,137(3):4794-4800
The paper presents new upper and lower bounds for the singular values of rectangularmatrices explicitly involving the matrix
sparsity pattern. These bounds are based on an upper bound for the Perron root of a nonnegative matrix and on the sparsity-dependent
version of the Ostrowski-Brauer theorem on eigenvalue inclusion regions. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 57–68. 相似文献