Convergence of Derivatives of Optimal Nodal Splines Original Research Article

Optimal nodal spline interpolantsWfof ordermwhich have local support can be used to interpolate a continuous functionfat a set of mesh points. These splines belong to a spline space with simple knots at the mesh points as well as atm−2 arbitrary points between any two mesh points and they reproduce polynomials of orderm. It has been shown that, for a sequence of locally uniform meshes, these splines converge uniformly for anyf∈Cas the mesh norm tends to zero. In this paper, we derive a set of sufficient conditions on the sequence of meshes for the uniform convergence ofDjWftoDjfforf∈Csandj=1, …, s