Accurate Computations Of Collocation Matrices Of Rational Bases

In this paper,we consider the high relative accuracy computation of singular values,eigenvalues and linear system solutions for totally non-positive rational Bernstein-Vandermonde matrices,and inverse totally non-positive rational BernsteinVandermonde matrices and rational Said-Ball-Vandermonde matrices.We first presented these three types of matrices.In chapter 2,we present an algorithm to compute accurately of singular values of rational Bernstein-Vandermonde totally non-positive matrices and exact solutions of linear systems are calculated.In the third chapter,the high-precision calculation problem of inverse totally non-positive collocation matrices of rational bases are discussed.For these three kinds of matrices,the Neville elimination method is used to bidiagonal decomposition and then re-parameterize and combine our existing algorithms for high-precision calculations.Finally,the accuracy of the algorithm is verified by numerical experiments.