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arXiv · 2303.01327

Noda Iteration for Computing Generalized Tensor Eigenpairs

Wanli Ma·Weiyang Ding·Yimin Wei
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Abstract

In this paper, we propose the tensor Noda iteration (NI) and its inexact version for solving the eigenvalue problem of a particular class of tensor pairs called generalized $\mathcal{M}$-tensor pairs. A generalized $\mathcal{M}$-tensor pair consists of a weakly irreducible nonnegative tensor and a nonsingular $\mathcal{M}$-tensor within a linear combination. It is shown that any generalized $\mathcal{M}$-tensor pair admits a unique positive generalized eigenvalue with a positive eigenvector. A modified tensor Noda iteration(MTNI) is developed for extending the Noda iteration for nonnegative matrix eigenproblems. In addition, the inexact generalized tensor Noda iteration method (IGTNI) and the generalized Newton-Noda iteration method (GNNI) are also introduced for more efficient implementations and faster convergence. Under a mild assumption on the initial values, the convergence of these algorithms is guaranteed. The efficiency of these algorithms is illustrated by numerical experiments.

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Wanli Ma, Weiyang Ding, Yimin Wei. 2023-03-02. Noda Iteration for Computing Generalized Tensor Eigenpairs. https://arxiv.org/abs/2303.01327

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