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On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors

On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors
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Year:    2021

Author:    Changxin Mo, Yimin Wei

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2020-0080

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 176–193

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

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

Author Details

Changxin Mo

Yimin Wei

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