Bounds and Inequalities for the Perron Root of a Nonnegative Matrix

被引：0

作者：

L. Yu. Kolotilina

机构：

[1] St.Petersburg Department of the Steklov Mathematical Institute,

来源：

Journal of Mathematical Sciences | 2004年 / 121卷 / 4期

关键词：

Monotonicity Property; Nonnegative Matrix; Classical Theorem; Perron Root;

D O I：

10.1023/B:JOTH.0000026286.68173.f4

中图分类号：

学科分类号：

摘要：

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.

引用

页码：2481 / 2507

页数：26

共 50 条

[31] Perron root bounding for nonnegative persymmetric matrices
Rojo, O
Soto, R
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1996, 31 (12) : 69 - 76
[32] Joint bounds for the Perron roots of nonnegative matrices with applications
Al'pin Yu.A.
Kolotilina L.Yu.
Korneeva N.N.
Journal of Mathematical Sciences, 2007, 141 (6) : 1586 - 1600
[33] THE INFLUENCE OF THE POSITION OF THE ZEROS IN A NONNEGATIVE MATRIX ON THE CONVERGENCE OF THE ALGORITHM FOR COMPUTING ITS PERRON ROOT
ZHUKOV, MY
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1994, 34 (05) : 665 - 670
[34] A simple proof for the inequality between the perron root of a nonnegative matrix and that of its geometric symmetrization
Alpin Y.A.
Merikoski J.K.
Lobachevskii Journal of Mathematics, 2010, 31 (3) : 222 - 223
[35] Some Inequalities Connecting the Singular Values of a Complex Matrix with the Perron Roots of Related Nonnegative Matrices
Kolotilina L.Y.
Journal of Mathematical Sciences, 2014, 199 (4) : 438 - 447
[36] Bounds for the Perron root of positive matrices
Liao, Ping
LINEAR & MULTILINEAR ALGEBRA, 2023, 71 (11): : 1849 - 1857
[37] Perron vectors of an irreducible nonnegative interval matrix
Rohn, Jiri
LINEAR & MULTILINEAR ALGEBRA, 2006, 54 (06): : 399 - 404
[38] BOUNDS FOR GREATEST CHARACTERISTIC ROOT OF AN IRREDUCIBLE NONNEGATIVE MATRIX .2.
BRAUER, A
GENTRY, IC
LINEAR ALGEBRA AND ITS APPLICATIONS, 1976, 13 (1-2) : 109 - 114
[39] THE PERRON ROOT OF A WEIGHTED GEOMETRIC MEAN OF NONNEGATIVE MATRICES
ELSNER, L
LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 104 : 213 - 216
[40] Some closer bounds of Perron root basing on generalized Perron complement
Yang, Zhi-Ming
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 235 (01) : 315 - 324

← 1 2 3 4 5 →