New Interval Estimates For Tensor H-eigenvalues And U-eigenvalues

This paper mainly studies the U-eigenvalue interval estimation of the tensor,and by the definition and properties of three new classes of structural tensors,we obtain three new intervals,which contain all the H-eigenvalues of real even order symmetric tensors.The full text is divided into four parts.In the first part,the research background of the tensor eigenvalue,eigenvalue inclusion interval and the current situation at home and abroad are introduced.In the second part,we explain some symbols used in this article.In the third part,we firstly introduce the definition of the U-eigenvalue,and give three interval estimates of the U-eigenvalue.The inclusion relationship among the three interval estimates is analyzed,and a better U-eigenvalue interval estimate is obtained.At last,a numerical example is used for simple verification.In the fourth part,we introduce the definition and properties of the _β~αΦ_S~+-tensor,QDB-tensor and SQDB-tensor,and then obtain three kinds of new structural tensors,namely (?)tensor,(?)-tensor and (?)-tensor.By studying their related properties,we obtain three new H-eigenvalue inclusion intervals of the even order real symmetric tensor.Finally,the relationship between the three new eigenvalue inclusion intervals and the existing (?)-interval,quasi-double (?)-interval is analysed.