A modified Newton iteration for finding nonnegative Z-eigenpairs of a nonnegative tensor

2017/05/21 by Chun‐Hua Guo, Guo, Chun-Hua, Wen‐Wei Lin +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1705.07487

openalex publication_date 2017/05/21 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

We propose a modified Newton iteration for finding some nonnegative Z-eigenpairs of a nonnegative tensor. When the tensor is irreducible, all nonnegative eigenpairs are known to be positive. We prove local quadratic convergence of the new iteration to any positive eigenpair of a nonnegative tensor, under the usual assumption guaranteeing the local quadratic convergence of the original Newton iteration. A big advantage of the modified Newton iteration is that it seems capable of finding a nonnegative eigenpair starting with any positive unit vector. Special attention is paid to transition probability tensors.

Citations

• On some properties of nonnegative weakly irreducible tensors
• Tensor Decompositions and Applications
• Perron–Frobenius theorem for nonnegative multilinear forms and extensions

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