On Lebesgue constants of local parabolic splines
The paper deals with the stability of a linear approximation method based on polynomial splines of minimal defect of degree with arbitrary knots. The stability is expressed in terms of the behavior of a uniform norm of a linear operator, called Lebesgue constant which, for a good stability, is aimed to be as small as possible with respect to a change in approximation conditions. The authors approach the method of local spline approximation as a useful alternative for the interpolation method taking into account the simplicity of construction, shape preserving property and smoothing properties. One issue addressed in the paper is to compare these two different approaches with respect to their stability to a change in the initial data and with respect to the value of Lebesgue constants. Two types of local parabolic splines are considered and in both cases, the Lebesgue constant is smaller than the corresponding constant for the interpolating parabolic splines.
scientific article; zbMATH DE number 6474036