共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
L.Yu. Kolotilina 《Linear algebra and its applications》2008,429(10):2521-2539
The paper considers the sharpness problem for certain two-sided bounds for the Perron root of an irreducible nonnegative matrix. The results obtained are applied to prove the sharpness of the related eigenvalue inclusion sets in classes of matrices with fixed diagonal entries, bounded above deleted absolute row sums, and a partly specified irreducible sparsity pattern. 相似文献
3.
Following the Perron theorem, the spectral radius of a primitive matrix is a simple eigenvalue. It is shown that for a primitive matrix A, there is a positive rank one matrix X such that B = A ° X , where ° denotes the Hadamard product of matrices, and such that the row (column) sums of matrix B are the same and equal to the Perron root. An iterative algorithm is presented to obtain matrix B without an explicit knowledge of X. The convergence rate of this algorithm is similar to that of the power method but it uses less computational load. A byproduct of the proposed algorithm is a new method for calculating the first eigenvector. 相似文献
4.
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
5.
Mirsolav Fiedler 《Linear and Multilinear Algebra》1973,1(1):81-88
A "measure of irreducibility" of a nonnegative matrix is introduced and applied to obtaining an estimate from below for the distance of the Perron eigenvalue from any other eigenvalue of such a matrix. 相似文献
6.
非负矩阵Perron根的估计是非负矩阵理论研究的重要课题之一.如果其上下界能够表示为非负矩阵元素的易于计算的函数,那么这种估计价值更高.本文结合非负矩阵的迹分两种情况给出Perron根的下界序列,并且给出数值例子加以说明. 相似文献
7.
Vladimir R. Kostić Agnieszka Międlar Ljiljana Cvetković 《Numerical Linear Algebra with Applications》2016,23(2):272-290
The existing algorithms for computing the minimal Ger?gorin set are designed for small and medium size (irreducible) matrices and based on Perron root computations coupled with bisection method and sampling techniques. Here, we first discuss the drawbacks of the existing methods and present a new approach based on the modified Newton's method to find zeros of the parameter dependent left‐most eigenvalue of a Z‐matrix and a special curve tracing procedure. The advantages of the new approach are presented on several test examples that arise in practical applications. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
Thomas J. Laffey 《Linear algebra and its applications》2006,416(1):148-159
The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions for a list of complex numbers σ to be the spectrum of a nonnegative matrix. In this paper the problem is completely solved in the case when all numbers in the given list σ except for one (the Perron eigenvalue) have real parts smaller than or equal to zero. 相似文献
9.
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
10.
<正>1引言若A=(a_(ij)),其中a_(ij)≥0,我们则称A为非负矩阵.ρ(A)表示A的谱半径,当A≥0时,ρ(A)就是A的Perron根.众所周知,若A≥0,则r_(min)(A)≤ρ(A)≤r_(max)(A), 相似文献
11.
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
12.
In a previous work [5] the authors developed formulas for the second order partial derivatives of the Perron root as a function of the matrix entries at an essentially nonnegative and irreducible matrix. These formulas, which involve the group generalized inverse of an associated M-matrix, were used to investigate the concavity and convexity of the Perron root as a function of the entries. The authors now combine the above results together with an approach taken in an earlier joint paper [6] of the second author with L. Elsner and C. Johnson, and they develop formulas for the second order derivatives of an appropriately normalized Perron vector with respect to the matrix entries, which again are given in terms the group generalized inverse of an associated M-matrix. Convexity properties of the Perron vector as a function of the entries of the matrix are then examined. In addition, formulas for the first derivative of the Perron vector resulting from different normalizations of this eigenvector are also given. A by-product of one of these formulas yields that the group generalized inverse of a singular and irreducible M-matrix can be diagonally scaled to a matrix which is entrywise column diagonally dominant. 相似文献
13.
14.
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
15.
Mihály Pituk 《Journal of Mathematical Analysis and Applications》2006,322(2):1140-1158
Asymptotic relations between the solutions of a linear autonomous functional differential equation and the solutions of the corresponding perturbed equation are established. In the scalar case, it is shown that the existence of a nonoscillatory solution of the perturbed equation often implies the existence of a real eigenvalue of the limiting equation. The proofs are based on a recent Perron type theorem for functional differential equations. 相似文献
16.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,127(3):1988-2005
The paper suggests two-sided, upper, and lower circuit bounds for the Perron root of a nonnegative matrix, most of which are derived based on an extension of the monotonicity property of the Perron root established by Fiedler and Pták. Bibliography: 9 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 296, 2003, pp. 60–88. 相似文献
17.
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
18.
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
19.
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
20.
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