Journal of Applied Mathematics
Volume 2013 (2013), Article ID 407128, 8 pages
http://dx.doi.org/10.1155/2013/407128
Research Article

Rate of Convergence of Hermite-Fejér Interpolation on the Unit Circle

E. Berriochoa,1 A. Cachafeiro,2 J. Díaz,2 and E. Martínez-Brey2

1Departamento de Matemática Aplicada I, Facultad de Ciencias, Universidad de Vigo, 32004 Ourense, Spain
2Departamento de Matemática Aplicada I, E. Ingeniería Industrial, Universidad de Vigo, 36310 Vigo, Spain

Received 13 November 2012; Revised 2 March 2013; Accepted 4 March 2013

Academic Editor: Roberto Barrio

Copyright © 2013 E. Berriochoa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper deals with the order of convergence of the Laurent polynomials of Hermite-Fejér interpolation on the unit circle with nodal system, the roots of a complex number with modulus one. The supremum norm of the error of interpolation is obtained for analytic functions as well as the corresponding asymptotic constants.