Estimation Of H-eigenvalues Of Even Order Real Symmetric Tensors

Tensors theory is one of the most important research topics in the field of multilinear numerical algebra,and has been widely used in many fields of scientific and engineering.In these applications,the location of H-eigenvalues of even order real symmetric tensors is often involved.In this thesis,by introducing two new structural tensors SD(?)-tensors and SQ(?)-tensors and studying their properties,we obtain two new inclusion intervals,SD(?)-interval and SQ(?)-interval for H-eigenvalues of even order real symmetric tensors.It is proved that the obtained SD(?)-interval and SQ(?)-interval are included in the H-eigenvalues inclusion intervals of real symmetric tensors given in [Hongwei Jin,M.Rajesh Kannan,Minru Bai,Lower and upper bounds for H-eigenvalues of even order real symmetric tensors,Linear and Multilinear Algebra.(2017)].