Convergence of Derivatives of Optimal Nodal Splines

Abstract

Optimal nodal spline interpolants Wf of order m which have local support can be used to interpolate a continuous function f at a set of mesh points. These splines belong to a spline space with simple knots at the mesh points as well as at m&2 arbitrary points between any two mesh points and they reproduce polynomials of order m. It has been shown that, for a sequence of locally uniform meshes, these splines converge uniformly for any f # C as 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 of D j

Peano Kernel Error Analysis for Quadratic Nodal Spline Interpolation

“…Also, in [8], it was shown that, in the context of quadrature rules, nodal spline interpolation yields an interpolant for the Gregory rule, which is an important example of a trapezoidal rule with endpoint corrections. Other recent papers in which the approximation properties and applications in quadrature of nodal spline interpolation were further explored, include those by Rabinowitz [10,11], Demichelis [4], and Dagnino et al [2]. Fundamental existence and uniqueness theorems for spline interpolation by means of additional knots, including the nodal spline case, were proved by Dahmen et al [3], and an explicit construction procedure for some of these spline interpolation operators was introduced by Chui and de Villiers in [1].…”