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# B tensors and tensor complementarity problems

Submit Time: 2017-07-25
Author: Yisheng Song Henan Normal University ; Wei Mei Henan Normal University ;
Institute: 1.河南师范大学数学与信息科学学院;

## Abstracts

 In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose, firstly, we present that each B tensor is strictly semi-positive and each B$_0$ tensor is semi-positive. Subsequencely, the strictly lower and upper bounds of different operator norms are given for two positively homogeneous operators defined by B tensor. Finally, with the help of the upper bounds of different operator norms, we show the strcitly lower bound of solution set of tensor complementarity problem with B tensor. Furthermore, the upper bounds of spectral radius and $E$-spectral radius of B (B$_0$) tensor are obtained, respectively, which achieves our another objective. In particular, such the upper bounds only depend on the principal diagonal entries of tensors.
From: 宋义生
DOI：10.12074/201707.00007
Recommended references： Yisheng Song,Wei Mei.(2017).B tensors and tensor complementarity problems.[ChinaXiv:201707.00007] (Click&Copy)
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