Uniqueness and perturbation bounds for sparse non-negative tensor equations

doi:10.1007/s11464-018-0707-y

Front. Math. China

2018, Vol. 13

Issue (4) : 849-874 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 LI²(

), Michael K. NG³, Seak-Weng VONG⁴

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

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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.

Keywords Stochastic tensor tensor equation uniqueness perturbation

Corresponding Author(s): Wen LI

Issue Date: 14 August 2018

Cite this article:

Dongdong LIU,Wen LI,Michael K. NG, et al. Uniqueness and perturbation bounds for sparse non-negative tensor equations[J]. Front. Math. China, 2018, 13(4): 849-874.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0707-y
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I4/849

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