Perron-Frobenius theorem for nonnegative multilinear forms and extensions

S. Friedland; S. Gaubert; L. Han

doi:10.1016/j.laa.2011.02.042

Perron-Frobenius theorem for nonnegative multilinear forms and extensions

S. Friedland
, S. Gaubert
, L. Han

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.

langue originale	Anglais
Pages (de - à)	738-749
Nombre de pages	12
journal	Linear Algebra and Its Applications
Volume	438
Numéro de publication	2
Les DOIs	https://doi.org/10.1016/j.laa.2011.02.042
état	Publié - 15 janv. 2013

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10.1016/j.laa.2011.02.042

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title = "Perron-Frobenius theorem for nonnegative multilinear forms and extensions",

abstract = "We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.",

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author = "S. Friedland and S. Gaubert and L. Han",

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AU - Friedland, S.

AU - Gaubert, S.

AU - Han, L.

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N2 - We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.

AB - We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.

KW - Convergence of the power algorithm

KW - Perron-Frobenius theorem for nonnegative tensors

UR - https://www.scopus.com/pages/publications/84869482453

U2 - 10.1016/j.laa.2011.02.042

DO - 10.1016/j.laa.2011.02.042

M3 - Article

AN - SCOPUS:84869482453

SN - 0024-3795

VL - 438

SP - 738

EP - 749

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2

ER -

Perron-Frobenius theorem for nonnegative multilinear forms and extensions

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