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Perron-Frobenius theorem for nonnegative multilinear forms and extensions

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arxiv 0905.1626 v3 pith:Z7IR6CFI submitted 2009-05-11 math.SP cs.NAmath.NA

S. Friedland , S. Gaubert , L. Han This is my paper · ORCID
classification math.SPcs.NAmath.NA
keywords nonnegativecoefficientsformsmultilinearperron-frobeniustheoremalgorithmanalog
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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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  1. Tropical Analysis of the Asymptotics of the Perron-Frobenius Eigenvector

    math.RA 2019-08 reject novelty 5.0 of 10

    The normalized Perron eigenvector of exp(kA) converges to a point in the tropical max-plus eigenspace, and two conjectures locate that point from the shape of the eigenspace.

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