Linear convergence of the LZI algorithm for weakly positive tensors

Liping Zhang; Liqun Qi; Yi Xu

doi:10.4208/jcm.1110-m11si09

Linear convergence of the LZI algorithm for weakly positive tensors

Liping Zhang, Liqun Qi, Yi Xu

Research output: Journal article publication › Journal article › Academic research › peer-review

36 Citations (Scopus)

Abstract

We define weakly positive tensors and study the relations among essentially positive tensors, weakly positive tensors, and primitive tensors. In particular, an explicit linear convergence rate of the Liu-Zhou-Ibrahim(LZI) algorithm for finding the largest eigenvalue of an irreducible nonnegative tensor, is established for weakly positive tensors. Numerical results are given to demonstrate linear convergence of the LZI algorithm for weakly positive tensors.

Original language	English
Pages (from-to)	24-33
Number of pages	10
Journal	Journal of Computational Mathematics
Volume	30
Issue number	1
DOIs	https://doi.org/10.4208/jcm.1110-m11si09
Publication status	Published - 1 Jan 2012

Keywords

Irreducible nonnegative tensor
Largest eigenvalue
Linear convergence
Weakly positive tensor

ASJC Scopus subject areas

Computational Mathematics

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10.4208/jcm.1110-m11si09

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AU - Xu, Yi

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AB - We define weakly positive tensors and study the relations among essentially positive tensors, weakly positive tensors, and primitive tensors. In particular, an explicit linear convergence rate of the Liu-Zhou-Ibrahim(LZI) algorithm for finding the largest eigenvalue of an irreducible nonnegative tensor, is established for weakly positive tensors. Numerical results are given to demonstrate linear convergence of the LZI algorithm for weakly positive tensors.

KW - Irreducible nonnegative tensor

KW - Largest eigenvalue

KW - Linear convergence

KW - Weakly positive tensor

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Linear convergence of the LZI algorithm for weakly positive tensors

Abstract

Keywords

ASJC Scopus subject areas

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