Localization of Perron roots

Linzhang Lu; Michael K. Ng

doi:10.1016/j.laa.2004.06.016

Localization of Perron roots

Linzhang Lu
, Michael K. Ng^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

12 Citations (Scopus)

Abstract

This paper is concerned with the localization of the Perron root of a nonnegative irreducible matrix A. A new localization method that utilizes the relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complement is presented. The method is efficient because it gives the bounds on ρ(A) only by computing the estimates of the row sums of the generalized Perron complement rather than the generalized Perron complement itself. Several numerical examples are given to illustrate the effectiveness of our method.

Original language	English
Pages (from-to)	103-117
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	392
Early online date	3 Aug 2004
DOIs	https://doi.org/10.1016/j.laa.2004.06.016
Publication status	Published - 15 Nov 2004

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User-Defined Keywords

Nonnegative irreducible matrix
Perron complement and Perron root
Spectral radius

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10.1016/j.laa.2004.06.016

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@article{003cb94e829b4db1bebd0fa15da4ac38,

title = "Localization of Perron roots",

abstract = "This paper is concerned with the localization of the Perron root of a nonnegative irreducible matrix A. A new localization method that utilizes the relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complement is presented. The method is efficient because it gives the bounds on ρ(A) only by computing the estimates of the row sums of the generalized Perron complement rather than the generalized Perron complement itself. Several numerical examples are given to illustrate the effectiveness of our method.",

keywords = "Nonnegative irreducible matrix, Perron complement and Perron root, Spectral radius",

author = "Linzhang Lu and Ng, \{Michael K.\}",

note = "Research supported in part by RGC Grant Nos. 7130/02P and 7046/03P, and HKU CRCG Grant Nos. 10203501 and 10204437 Publisher Copyright: {\textcopyright} 2004 Elsevier Inc. All rights reserved.",

year = "2004",

month = nov,

day = "15",

doi = "10.1016/j.laa.2004.06.016",

language = "English",

volume = "392",

pages = "103--117",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

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TY - JOUR

T1 - Localization of Perron roots

AU - Lu, Linzhang

AU - Ng, Michael K.

PY - 2004/11/15

Y1 - 2004/11/15

N2 - This paper is concerned with the localization of the Perron root of a nonnegative irreducible matrix A. A new localization method that utilizes the relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complement is presented. The method is efficient because it gives the bounds on ρ(A) only by computing the estimates of the row sums of the generalized Perron complement rather than the generalized Perron complement itself. Several numerical examples are given to illustrate the effectiveness of our method.

AB - This paper is concerned with the localization of the Perron root of a nonnegative irreducible matrix A. A new localization method that utilizes the relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complement is presented. The method is efficient because it gives the bounds on ρ(A) only by computing the estimates of the row sums of the generalized Perron complement rather than the generalized Perron complement itself. Several numerical examples are given to illustrate the effectiveness of our method.

KW - Nonnegative irreducible matrix

KW - Perron complement and Perron root

KW - Spectral radius

UR - https://www.scopus.com/pages/publications/5444247873

UR - https://www.sciencedirect.com/science/article/pii/S0024379504002939?via%3Dihub

U2 - 10.1016/j.laa.2004.06.016

DO - 10.1016/j.laa.2004.06.016

M3 - Journal article

AN - SCOPUS:5444247873

SN - 0024-3795

VL - 392

SP - 103

EP - 117

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Localization of Perron roots

Abstract

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