Geodesic
Explicit formulas for Hermite-type interpolation on the circle and applications
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 140-152.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 65D05, 41A05, 33C45
Keywords: Hermite interpolation, Laurent polynomials, barycentric formulas, unit circle, Chebyshev polynomials 
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     title = {Explicit formulas for {Hermite-type} interpolation on the circle and applications},
     journal = {Electronic transactions on numerical analysis},
     pages = {140--152},
     publisher = {mathdoc},
     volume = {44},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a23/}
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Berriochoa, Elías; Cachafeiro, Alicia; Díaz, Jaime; Illán, Jesús. Explicit formulas for Hermite-type interpolation on the circle and applications. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 140-152. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a23/