Volume 44, pp. 140-152, 2015.

Explicit formulas for Hermite-type interpolation on the circle and applications

Elías Berriochoa, Alicia Cachafeiro, Jaime Díaz, and Jesús Illán

Abstract

In this paper we study two ways of obtaining Laurent polynomials of Hermite interpolation on the unit circle. The corresponding nodal system is constituted by the $n$th roots of a complex number with modulus one. One of the interpolation formulas is given in terms of an appropriate basis which yields coefficients computable by means of the fast Fourier transform (FFT). The other formula is of barycentric type. As a consequence, we illustrate some applications to the Hermite interpolation problem on $[-1,1]$. Some numerical tests are presented to emphasize the numerical stability of these formulas.

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Key words

Hermite interpolation, Laurent polynomials, barycentric formulas, unit circle, Chebyshev polynomials

AMS subject classifications

65D05, 41A05, 33C45