| The tensor eigenvalue complementarity problems are the generalization of the matrix eigenvalue complementarity problems and the tensor eigenvalue problems,it is closely related to polynomial optimization.The problem are widely used in big data processing,engineering technology,medical imaging,economics and other fields.Given the estimation of tensor eigenvalues are widely used in data analysis,statistics,images processing and other fields,so it is of great significance to estimate the eigenvalues of tensors.In this regard,based on the related theories of tensor Pareto eigenvalues,this paper studies Pareto Z-eigenvalue inclusion set and strict copositivity of tensors,and obtains some valuable results.Specifically,the main research contents and results obtained in this paper are as follows:Chapter Ⅰ introduces the research background of tensor eigenvalue complementarity problem and the recent research situation at home and abroad,and gives some definitions of tensor Z-eigenvalue complementarity problem.Chapter Ⅱ the inclusion sets of several Pareto Z-eigenvalues are obtained by extracting the element information of the tensor,and the comparison between different Pareto Z-eigenvalue inclusion sets is established.In particular,this paper give sufficient and testable conditions for the strict copositivity of symmetric tensors.The numerical examples given show the validity of the conclusions obtained.Chapter Ⅲ explores the relationship between tensors and their induced matrices by mining tensor structure information,and the spectral radius of the corresponding symmetric matrix is used to establish the Pareto Z-eigenvalue inclusion sets.As an application,sufficient conditions for strict copositivity of symmetric tensors are proposed.Chapter Ⅳ briefly conclude the content of this paper and proposes topics that can be studied in the future. |
