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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	738-749
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	2
DOIs	https://doi.org/10.1016/j.laa.2011.02.042
Publication status	Published - 15 Jan 2013

Keywords

Convergence of the power algorithm
Perron-Frobenius theorem for nonnegative tensors

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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 - 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

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DO - 10.1016/j.laa.2011.02.042

M3 - Article

AN - SCOPUS:84869482453

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VL - 438

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EP - 749

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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Perron-Frobenius theorem for nonnegative multilinear forms and extensions

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Keywords

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