Journal of Applied Mathematics
Volume 2012 (2012), Article ID 421340, 11 pages
http://dx.doi.org/10.1155/2012/421340
Research Article

About Nodal Systems for Lagrange Interpolation on the Circle

E. Berriochoa,1 A. Cachafeiro,2 and J. M. García Amor2

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

Received 20 July 2011; Accepted 12 October 2011

Academic Editor: Nicola Guglielmi

Copyright © 2012 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

We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are more general than those constituted by the n roots of complex unimodular numbers and the class of functions is different from the usually studied. Moreover, some consequences for the Lagrange interpolation on [ − 1 , 1 ] and the Lagrange trigonometric interpolation are obtained.