Geodesic
Explicit formulas for Hermite-type interpolation on the circle and applications
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 140-152
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 
@article{ETNA_2015__44__a23,
     author = {Berriochoa,  El{\'\i}as and Cachafeiro,  Alicia and D{\'\i}az,  Jaime and Ill\'an,  Jes\'us},
     title = {Explicit formulas for {Hermite-type} interpolation on the circle and applications},
     journal = {Electronic transactions on numerical analysis},
     pages = {140--152},
     year = {2015},
     volume = {44},
     zbl = {1312.65012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a23/}
}
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AU  - Cachafeiro,  Alicia
AU  - Díaz,  Jaime
AU  - Illán,  Jesús
TI  - Explicit formulas for Hermite-type interpolation on the circle and applications
JO  - Electronic transactions on numerical analysis
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EP  - 152
VL  - 44
UR  - http://geodesic.mathdoc.fr/item/ETNA_2015__44__a23/
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%A Cachafeiro,  Alicia
%A Díaz,  Jaime
%A Illán,  Jesús
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%J Electronic transactions on numerical analysis
%D 2015
%P 140-152
%V 44
%U http://geodesic.mathdoc.fr/item/ETNA_2015__44__a23/
%G en
%F ETNA_2015__44__a23
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/