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Further study on tensor absolute value equations

  • Chen Ling
  • Weijie Yan
  • Hongjin HeEmail author
  • Liqun Qi
Article

Abstract

In this paper, we consider the tensor absolute value equations (TAVEs), which is a newly introduced problem in the context of multilinear systems. Although the system of the TAVEs is an interesting generalization of matrix absolute value equations (AVEs), the well-developed theory and algorithms for the AVEs are not directly applicable to the TAVEs due to the nonlinearity (or multilinearity) of the problem under consideration. Therefore, we first study the solutions existence of some classes of the TAVEs with the help of degree theory, in addition to showing, by fixed point theory, that the system of the TAVEs has at least one solution under some checkable conditions. Then, we give a bound of solutions of the TAVEs for some special cases. To find a solution to the TAVEs, we employ the generalized Newton method and report some preliminary results.

Keywords

tensor absolute value equations H+-tensor P-tensor copositive tensor generalized Newton method 

MSC(2010)

15A48 15A69 65K05 90C30 90C20 

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Notes

Acknowledgements

The first author and the third author were supported by National Natural Science Foundation of China (Grant Nos. 11571087 and 11771113) and Natural Science Foundation of Zhejiang Province (Grant No. LY17A010028). The fourth author was supported by the Hong Kong Research Grant Council (Grant Nos. PolyU 15302114, 15300715, 15301716 and 15300717).

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceHangzhou Dianzi UniversityHangzhouChina
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina

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