Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4639756 | Journal of Computational and Applied Mathematics | 2011 | 11 Pages |
Abstract
As a continuation of the well known connection between the theory of orthogonal polynomials on the unit circle and the interval [−1,1][−1,1], in this paper properties concerning error and convergence of certain rational approximants associated with the measures dμ(t) and dσ(θ)=|dμ(cosθ)| supported on [−1,1][−1,1] and the unit circle respectively are deduced. Numerical illustrations are also given.
► We analyze a connection between certain rational approximants to Markov functions and to Herglotz–Riesz transform. ► We compute rational approximats from Szegő quadrature formulas. ► Error estimates and convergence are analyzed. ► An application to the numerical calculation of certain special functions is carried out.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Ruymán Cruz-Barroso, Pablo González-Vera, Francisco Perdomo-Pío,