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

E. Berriochoa | Zendy; A. Cachafeiro | Zendy; Jaime Díaz | Zendy

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

Author(s) -

E. Berriochoa,

A. Cachafeiro,

Jaime Díaz

Publication year - 2014

Publication title -

isrn mathematical analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-4665

pISSN - 2090-4657

DOI - 10.1155/2014/808519

Subject(s) - hermite interpolation , mathematics , unit circle , interpolation (computer graphics) , trigonometric interpolation , laurent polynomial , barycentric coordinate system , birkhoff interpolation , laurent series , polynomial interpolation , hermite polynomials , polynomial , algebra over a field , pure mathematics , mathematical analysis , linear interpolation , geometry , computer science , animation , computer graphics (images)

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.

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