English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

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

Noda Iteration for Computing Generalized Tensor Eigenpairs