New error bounds for the tensor complementarity problem

Xin Liu; Guang-Xin Huang; Xin Liu; Guang-Xin Huang

doi:10.3934/era.2022111

Electronic Research Archive

2022, Volume 30, Issue 6: 2196-2204. doi: 10.3934/era.2022111

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New error bounds for the tensor complementarity problem

Xin Liu ,
Guang-Xin Huang ^,

College of Mathematics and Physics, Geomathematics Key Laboratory of Sichuan, Chengdu University of Technology, Chengdu 610059, China

Academic Editor: Xian-Ming Gu

Received: 31 December 2021 Revised: 02 April 2022 Accepted: 04 April 2022 Published: 20 April 2022

This paper discusses new error bounds for the tensor complementarity problem using a $ P $-tensor. A new lower error bound and a global error bound are presented for such a problem. It is proved that the norm of the exact solution of the tensor complementarity problem with a $ P $-tensor has a lower bound and an upper bound. When the order of a tensor is $ 2 $, all the results for the tensor complementarity problem obtained reduce to those for the linear complementarity problem.
- tensor complementarity problem,
- $ P $-tensor,
- error bound,
- linear complementarity problem,
- $ P $-matrix
Citation: Xin Liu, Guang-Xin Huang. New error bounds for the tensor complementarity problem[J]. Electronic Research Archive, 2022, 30(6): 2196-2204. doi: 10.3934/era.2022111

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Abstract

This paper discusses new error bounds for the tensor complementarity problem using a $ P $-tensor. A new lower error bound and a global error bound are presented for such a problem. It is proved that the norm of the exact solution of the tensor complementarity problem with a $ P $-tensor has a lower bound and an upper bound. When the order of a tensor is $ 2 $, all the results for the tensor complementarity problem obtained reduce to those for the linear complementarity problem.

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