Strict Copositivity for a Class of Fourth-Order Three-Dimensional Tensors

Abstract

This paper focuses on the strict copositivity of fourth-order three-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, we discuss the strict copositivity of fourth-order three-dimensional symmetric tensors with their entries

\pm 1,0

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\pm 1, 0$$\end{document}

and further build their necessary and sufficient conditions. Utilizing these theorems, we can effectively verify the strict copositivity of general fourth-order three-dimensional symmetric tensors.

Keywords

Analysis conditions / Strictly copositive / Symmetric tensors / Fourth-order tensors / 90C23 / 15A69 / 15A72 / 90C30

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Funding

National Natural Science Foundation of P.R. China(12171064)

RIGHTS & PERMISSIONS

Shanghai University

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