Accurate Computations Of Eigenvalues And Singular Values Of Several Classes Of Vandermonde Matrices

In this thesis,several classes of Vandermonde matrices are studied,which includes high relative accuracy of singular values and eigenvalues of h-Bernstein-Vandermonde-like totally nonpositive matrices and Generalized-h-Bernstein-Vandermonde inverse totally nonpositive matrices.In this thesis,the parametrization of h-Bernstein-Vandermonde-like totally nonpositive matrices and Generalized-h-Bernstein-Vandermonde inverse totally nonpositive matrices are given;then,the algorithms of high relative accuracy are provided for numerical computation of these two special matrices;finally,numerical example shows that the algorithms are highly accurate.The specific arrangement of this thesis is as follows:In chapter one,the background and research status of structural matrix are introduced,and explain the symbols needed in this thesis,as well as provide the basic conclusions of Neville elimination method and h-Bernstein-Vandermonde matrices.In chapter two,the parametric characterization of h-Bernstein-Vandermonde-like totally nonpositive matrices is given;then,the algorithms are designed for calculating all singular values of the kind of matrices with high relative accuracy;finally,numerical example shows that the algorithms are highly accurate.In chapter three,the parametric characterization of h-Bernstein-Vandermonde inverse totally nonpositive matrices is given;then,the corresponding algorithms are designed for calculating all eigenvalues and singular values of the kind of matrices with high relative accuracy;finally,numerical example shows that the algorithms are highly accurate.In chapter four,this thesis briefly describes the main conclusions,and puts forward the prospect of the research on the high relative accuracy calculation of other related numerical algebra problems of totally nonpositive matrices and inverse totally nonpositive matrices.