Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 4: 849 - 874

DOI: https://doi.org/10.1007/s11464-018-0707-y

RESEARCH ARTICLE

Uniqueness and perturbation bounds for sparse non-negative tensor equations

  • Dongdong LIU 1,4 ,
  • Wen LI , 2 ,
  • Michael K. NG 3 ,
  • Seak-Weng VONG 4
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  • 1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China
  • 2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • 3. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
  • 4. Department of Mathematics, University of Macau, Macau, China

Received date: 20 Apr 2017

Accepted date: 25 May 2018

Published date: 14 Aug 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the uniqueness of the solution of the tensor equation. On the other hand, we present some perturbation bounds for the tensor equation. Numerical examples are given to show the effciency of the theoretical results.

Key words： Stochastic tensor; tensor equation; uniqueness; perturbation

Cite this article

Dongdong LIU , Wen LI , Michael K. NG , Seak-Weng VONG . Uniqueness and perturbation bounds for sparse non-negative tensor equations[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 849 -874 . DOI: 10.1007/s11464-018-0707-y

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