The Perron-Frobenius theorem for multi-homogeneous maps

Gautier Antoine, Francesco Tudisco, Matthias Hein

Research output: Working paper

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.
Original languageEnglish
Place of PublicationIthaca, NY
Number of pages54
Publication statusPublished - 10 Feb 2017

Keywords

  • functional analysis
  • numerical analysis
  • Perron-Frobenius theorem

Cite this

Antoine, G., Tudisco, F., & Hein, M. (2017). The Perron-Frobenius theorem for multi-homogeneous maps.