Volume 30, Issue 1
Linear Convergence of the LZI Algorithm for Weakly Positive Tensors

Liping Zhang, Liqun Qi & Yi Xu

J. Comp. Math., 30 (2012), pp. 24-33

Published online: 2012-02

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Irreducible nonnegative tensor Weakly positive tensor Largest eigenvalue Linear convergence

  • AMS Subject Headings

74B99 15A18 15A69.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-24, author = {Liping Zhang, Liqun Qi and Yi Xu}, title = {Linear Convergence of the LZI Algorithm for Weakly Positive Tensors}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {1}, pages = {24--33}, 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.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1110-m11si09}, url = {http://global-sci.org/intro/article_detail/jcm/8414.html} }
TY - JOUR T1 - Linear Convergence of the LZI Algorithm for Weakly Positive Tensors AU - Liping Zhang, Liqun Qi & Yi Xu JO - Journal of Computational Mathematics VL - 1 SP - 24 EP - 33 PY - 2012 DA - 2012/02 SN - 30 DO - http://doi.org/10.4208/jcm.1110-m11si09 UR - https://global-sci.org/intro/article_detail/jcm/8414.html KW - Irreducible nonnegative tensor KW - Weakly positive tensor KW - Largest eigenvalue KW - Linear convergence 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.
Liping Zhang, Liqun Qi & Yi Xu. (1970). Linear Convergence of the LZI Algorithm for Weakly Positive Tensors. Journal of Computational Mathematics. 30 (1). 24-33. doi:10.4208/jcm.1110-m11si09
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