Some New Inclusion Sets For Chebyshev Polynomial Zeros

As a kind of generalized polynomials,Chebyshev polynomial has many applications in the fields of data fitting,series expansion,interpolating and so on.Polynomial zeros estimation has a great significance in the study and application of the properties of polynomials.So it is necessary to estimate Chebyshev polynomial zeros.On the other hand,Chebyshev polynomial zeros are consistent with the eigenvalues of their comrade matrix,which provides a theoretical basis for studying Chebyshev polynomial zeros by using matrix theory.In this thesis,we use the Gershgorin theorem and Brauer theorem on inclusion sets for the eigenvalues of matrix and the properties of similar matrix and ovals of Cassini to derive some estimations of Chebyshev polynomial zeros.Besides,we explain these results are sharper than that obtained by using Gershgorin theorem and Melman's result in [Linear Algebra and its Applications,445(2014)326-346] by theoretical and examples.