Error bounds for a convexity-preserving interpolation and its limit function

Authors:
S. Amat;K. Dadourian;R. Donat;J. Liandrat;J. C. Trillo
Affiliations:
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;Ecole Généraliste d'Ingénieurs de Marseille (EGIM), Laboratoire d'Analyse Topologie et Probabilites, France;Departamento de Matemática Aplicada, Universidad de Valencia, Spain;Ecole Généraliste d'Ingénieurs de Marseille (EGIM), Laboratoire d'Analyse Topologie et Probabilites, France;Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

Error bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.