Table of Contents
ISRN Mathematical Analysis
Volume 2014, Article ID 808519, 10 pages
http://dx.doi.org/10.1155/2014/808519
Research Article

Hermite Interpolation on the Unit Circle Considering up to the Second Derivative

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 18 December 2013; Accepted 8 January 2014; Published 10 March 2014

Academic Editors: G. Ólafsson and T. Tran

Copyright © 2014 Elías 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 is devoted to study the Hermite interpolation problem on the unit circle. The interpolation conditions prefix the values of the polynomial and its first two derivatives at the nodal points and the nodal system is constituted by complex numbers equally spaced on the unit circle. We solve the problem in the space of Laurent polynomials by giving two different expressions for the interpolation polynomial. The first one is given in terms of the natural basis of Laurent polynomials and the remarkable fact is that the coefficients can be computed in an easy and efficient way by means of the Fast Fourier Transform (FFT). The second expression is a barycentric formula, which is very suitable for computational purposes.