Pseudospectra localization sets of tensors with applications

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:369

Article

He, Jun¹  Li, Chaoqian²  Wei, Yimin^3,4 

[1] Zunyi Normal Coll, Sch Math, Zunyi 563006, Guizhou, Peoples R China

[2] Yunnan Univ, Sch Math & Stat, Kunming 650091, Yunnan, Peoples R China

[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[4] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

关键词: Pseudospectra localization;    Asymptotically stable;    Homogeneous dynamical system;    Preservation measure;    Tensor complementarity problems;    Copositivity;   

DOI  :  10.1016/j.cam.2019.112580

来源: Elsevier

【 摘 要 】

A localization set and an exclusion set for the pseudospectrum of tensors are given. As applications, we first use the pseudospectra localization sets to locate asymptotically stable sets for homogeneous dynamical systems, and then two upper bounds for the largest modulus of the asymptotically stable set are given to estimate the asymptotic decay rate for homogeneous dynamical systems. We also provide two lower bounds for the preservation measure to the positive definiteness of the homogeneous polynomial form. In addition, some sufficient conditions for the global uniqueness and solvability of tensor complementarity problems are presented. The last application is to test copositivity of some potential fields in particle physics. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free