Some examples of quasi-interpolants constructed from local spline projectors

Abstract

Abstract. We give a recipe for deriving local spline approximation meth-ods which reproduce the whole spline space. The methods are obtained by solving a series of local approximation problems. Examples of specic quadratic and cubic approximation methods are given. Many applications of splines make use of some approximation method to pro-duce a spline function from given discrete data. Popular methods include interpolation and least squares approximation. However, both of these meth-ods require solution of a linear system of equations with as many unknowns as