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Volume 2, Issue 2
The Projected Newton Iteration Approach for Computing the Nonnegative Z-Eigenpairs of Nonnegative Tensors

Peihuan Bi, Wen Li, Dongdong Liu & Mingqing Xiao

DOI: 10.4208/csiam-am.2021.nla.07

CSIAM Trans. Appl. Math., 2 (2021), pp. 376-394.

Published online: 2021-05

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  • Abstract

In this paper, we propose a new projected Newton iteration for computing the nonnegative Z-eigenpairs of nonnegative tensors. We show that the required iteration has a local quadratic convergence. More specially, the formulation aims to solve the tensor equation arising from the multilinear PageRank problem. Numerical experiments are provided to illustrate the effectiveness and superiority of the proposed approach.

  • Keywords

Nonnegative tensor, nonnegative Z-eigenpair, local quadratic convergence, multilinear PageRank.

  • AMS Subject Headings

65F15, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-2-376, author = {Bi , PeihuanLi , WenLiu , Dongdong and Xiao , Mingqing}, title = {The Projected Newton Iteration Approach for Computing the Nonnegative Z-Eigenpairs of Nonnegative Tensors}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2021}, volume = {2}, number = {2}, pages = {376--394}, abstract = {

In this paper, we propose a new projected Newton iteration for computing the nonnegative Z-eigenpairs of nonnegative tensors. We show that the required iteration has a local quadratic convergence. More specially, the formulation aims to solve the tensor equation arising from the multilinear PageRank problem. Numerical experiments are provided to illustrate the effectiveness and superiority of the proposed approach.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2021.nla.07}, url = {http://global-sci.org/intro/article_detail/csiam-am/18890.html} }
TY - JOUR T1 - The Projected Newton Iteration Approach for Computing the Nonnegative Z-Eigenpairs of Nonnegative Tensors AU - Bi , Peihuan AU - Li , Wen AU - Liu , Dongdong AU - Xiao , Mingqing JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 376 EP - 394 PY - 2021 DA - 2021/05 SN - 2 DO - http://doi.org/10.4208/csiam-am.2021.nla.07 UR - https://global-sci.org/intro/article_detail/csiam-am/18890.html KW - Nonnegative tensor, nonnegative Z-eigenpair, local quadratic convergence, multilinear PageRank. AB -

In this paper, we propose a new projected Newton iteration for computing the nonnegative Z-eigenpairs of nonnegative tensors. We show that the required iteration has a local quadratic convergence. More specially, the formulation aims to solve the tensor equation arising from the multilinear PageRank problem. Numerical experiments are provided to illustrate the effectiveness and superiority of the proposed approach.

Bi , PeihuanLi , WenLiu , Dongdong and Xiao , Mingqing. (2021). The Projected Newton Iteration Approach for Computing the Nonnegative Z-Eigenpairs of Nonnegative Tensors. CSIAM Transactions on Applied Mathematics. 2 (2). 376-394. doi:10.4208/csiam-am.2021.nla.07
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