In order to approximate functions from their values at a discrete set of nodes on the sphere, we consider delayed means, of de la Vallée Poussin type, of least squares approximations. Similarly to the classical de la Vallée Poussin means, the resulting discrete operators are quasi polynomial projections. Moreover, under suitable assumptions on the given set of nodes, we state that the associated Lebesgue constants are uniformly bounded by a constant independent of the degree. Hence, we get near best polynomial approximations defined by the discrete set of values that the function to be approximate takes at a suitable set of points on the sphere.
Discrete de la Vallee Poussin approximation on the sphere
W Themistoclakis;
2014
Abstract
In order to approximate functions from their values at a discrete set of nodes on the sphere, we consider delayed means, of de la Vallée Poussin type, of least squares approximations. Similarly to the classical de la Vallée Poussin means, the resulting discrete operators are quasi polynomial projections. Moreover, under suitable assumptions on the given set of nodes, we state that the associated Lebesgue constants are uniformly bounded by a constant independent of the degree. Hence, we get near best polynomial approximations defined by the discrete set of values that the function to be approximate takes at a suitable set of points on the sphere.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
