The Perron-Frobenius Theorem for Multi-homogeneous Maps

Antoine Gautier; Francesco Tudisco; Matthias Hein

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arXiv · 1702.03230

The Perron-Frobenius Theorem for Multi-homogeneous Maps

Antoine Gautier·Francesco Tudisco·Matthias Hein

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Abstract

We introduce the notion of order-preserving multi-homogeneous mapping which allows to study Perron-Frobenius type theorems and nonnegative tensors in unified fashion. We prove a weak and strong Perron-Frobenius theorem for these maps and provide a Collatz-Wielandt principle for the maximal eigenvalue. Additionally, we propose a generalization of the power method for the computation of the maximal eigenvector and analyse its convergence. We show that the general theory provides new results and strengthens existing results for various spectral problems for nonnegative tensors.

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BibTeX RIS

Antoine Gautier, Francesco Tudisco, Matthias Hein. 2017-02-10. The Perron-Frobenius Theorem for Multi-homogeneous Maps. https://arxiv.org/abs/1702.03230

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