Convergence of Hermite interpolants on the circle using two derivatives

• E. Berriochoa ^[1] ; A. Cachafeiro ^[1] ; Jaime Díaz de Bustamante
  1. [1] Universidade de Vigo

     Universidade de Vigo

     Vigo, España

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 284, Nº 1 (15 August 2015), 2015, págs. 58-68
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.10.001
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• Resumen

  • In this paper we deal with Hermite interpolation problems on the unit circle considering up to the second derivative for the interpolation conditions and taking equally spaced points as nodal system. In the extended Fejér case, which corresponds to take vanishing values for the first two derivatives, we prove the uniform convergence for the interpolants related to continuous functions with smooth modulus of continuity. We also consider the Hermite case with non vanishing conditions for the derivatives for which we establish sufficient conditions on the interpolation conditions to obtain convergence.