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Journal Articles Linear Algebra and its Applications Year : 2013

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.

Dates and versions

hal-00782755 , version 1 (30-01-2013)

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S. Friedland, Stéphane Gaubert, L. Han. Perron--Frobenius theorem for nonnegative multilinear forms and extensions. Linear Algebra and its Applications, 2013, 438 (2), pp.738-749. ⟨10.1016/j.laa.2011.02.042⟩. ⟨hal-00782755⟩
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