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 unique...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 efficiency of the theoretical results.展开更多
In this paper,we propose a bound for ratio of the largest eigenvalue and second largest eigenvalue in module for a higher-order tensor.From this bound,one may deduce the bound of the second largest eigenvalue in modul...In this paper,we propose a bound for ratio of the largest eigenvalue and second largest eigenvalue in module for a higher-order tensor.From this bound,one may deduce the bound of the second largest eigenvalue in module for a positive tensor,and the bound can reduce to the matrix cases.展开更多
基金The authors would like to thank the referees for their helpful comments. The first author was supported by the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University （Grant No. 2018008） the second author was supported by the National Natural Science Foundation of China （Grant Nos. 11671185, 11771159）, and Major Project （Grant No. 2016KZDXM025）, and Innovation Team Project （Grant No. 2015KCXTD007） of Guangdong Provincial Universities+1 种基金 the third author was supported in part by HKBGC GRF 1202715, 12306616, 12200317 and HKBU RC-ICRS/16-17/03 the fourth author was supported by University of Macao （Grant No. MYRG2017-00098-FST） and the Macao Science and Technology Development Fund （050/2017/A）.
文摘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 efficiency of the theoretical results.
基金the National Natural Science Foundation of China(Nos.11271144 and 11671158)The third author was supported in part by University of Macao(No.MYRG2015-00064-FST).
文摘In this paper,we propose a bound for ratio of the largest eigenvalue and second largest eigenvalue in module for a higher-order tensor.From this bound,one may deduce the bound of the second largest eigenvalue in module for a positive tensor,and the bound can reduce to the matrix cases.
