## Abstract

We propose an inverse iterative method for computing the Perron pair of an irreducible nonnegative third order tensor. The method involves the selection of a parameter θ_{k} in the kth iteration. For every positive starting vector, the method converges quadratically and is positivity preserving in the sense that the vectors approximating the Perron vector are strictly positive in each iteration. It is also shown that θ_{k} = 1 near convergence. The computational work for each iteration of the proposed method is less than four times (three times if the tensor is symmetric in modes two and three, and twice if we also take the parameter to be 1 directly) that for each iteration of the Ng-Qi-Zhou algorithm, which is linearly convergent for essentially positive tensors.

Original language | English |
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Pages (from-to) | 911-932 |

Number of pages | 22 |

Journal | SIAM Journal on Matrix Analysis and Applications |

Volume | 37 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 2016 |

## Keywords

- Inverse iteration
- M-matrix
- Nonnegative matrix
- Nonnegative tensor
- Perron root
- Perron vector
- Positivity preserving
- Quadratic convergence