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Volume 14, Issue 1
On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors

Changxin Mo & Yimin Wei

DOI: 10.4208/nmtma.OA-2020-0080

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 176-193.

Published online: 2020-10

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  • Abstract

A class of structured multi-linear system defined by strong $\mathcal{M}_z$-tensors is considered. We prove that the multi-linear system with strong $\mathcal{M}_z$-tensors always has a nonnegative solution under certain condition by the fixed point theory. We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors, such as strong $\mathcal{M}$-tensors, $\mathcal{H}^+$-tensors, strictly diagonally dominant tensors with positive diagonal elements. Numerical examples are presented to illustrate our theoretical results.

  • Keywords

$\mathcal{M}_z$-tensor, multi-linear system, nonnegative solution, $\mathcal{M}$-tensor, tensor equation, fixed point theory.

  • AMS Subject Headings

15A18, 15A69

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-176, author = {Mo , Changxin and Wei , Yimin}, title = {On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {14}, number = {1}, pages = {176--193}, abstract = {

A class of structured multi-linear system defined by strong $\mathcal{M}_z$-tensors is considered. We prove that the multi-linear system with strong $\mathcal{M}_z$-tensors always has a nonnegative solution under certain condition by the fixed point theory. We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors, such as strong $\mathcal{M}$-tensors, $\mathcal{H}^+$-tensors, strictly diagonally dominant tensors with positive diagonal elements. Numerical examples are presented to illustrate our theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0080}, url = {http://global-sci.org/intro/article_detail/nmtma/18331.html} }
TY - JOUR T1 - On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors AU - Mo , Changxin AU - Wei , Yimin JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 176 EP - 193 PY - 2020 DA - 2020/10 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0080 UR - https://global-sci.org/intro/article_detail/nmtma/18331.html KW - $\mathcal{M}_z$-tensor, multi-linear system, nonnegative solution, $\mathcal{M}$-tensor, tensor equation, fixed point theory. AB -

A class of structured multi-linear system defined by strong $\mathcal{M}_z$-tensors is considered. We prove that the multi-linear system with strong $\mathcal{M}_z$-tensors always has a nonnegative solution under certain condition by the fixed point theory. We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors, such as strong $\mathcal{M}$-tensors, $\mathcal{H}^+$-tensors, strictly diagonally dominant tensors with positive diagonal elements. Numerical examples are presented to illustrate our theoretical results.

Mo , Changxin and Wei , Yimin. (2020). On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors. Numerical Mathematics: Theory, Methods and Applications. 14 (1). 176-193. doi:10.4208/nmtma.OA-2020-0080
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