Continuation Methods for Computing Z-/H-eigenpairs of Nonnegative Tensors

2017/02/20 by Yueh‐Cheng Kuo, Kuo, Yueh-Cheng, Wen‐Wei Lin +3
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1702.05841

openalex publication_date 2017/02/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.

Citations

• Most Tensor Problems Are NP-Hard

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