Approximation by local ℒ-splines that are exact on subspaces of the kernel of a differential operator

Abstract

We construct local ℒ-splines with uniform knots that preserve subsets from the kernel of a linear differential operator ℒ of order r with constant real coefficients and pairwise distinct roots of the characteristic polynomial. Pointwise estimates are found for the error of approximation by the constructed ℒ-splines on classes of functions defined by differential operators of orders smaller than r.