Perron–Frobenius theorem for nonnegative multilinear forms and extensions

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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Bibliographic Details
Published inLinear algebra and its applications Vol. 438; no. 2; pp. 738 - 749
Main Authors Friedland, S., Gaubert, S., Han, L.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2013
Elsevier
Subjects
15A48
47H07
47H09
47H10
Convergence of the power algorithm
Mathematics
Optimization and Control
Perron–Frobenius theorem for nonnegative tensors
47H09
Perron–Frobenius theorem for nonnegative tensors
Convergence of the power algorithm
47H10
15A48
47H07
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2011.02.042