A Convergence Result in Nodal Spline Interpolation Original Research Article

In this paper we study the property of uniform convergence for a certain nodal spline interpolation operator. After solving for the corresponding B-spline coefficients from a transposed Vandermonde linear system, we derive a Jackson-type estimate in which the dependence of the associated constants on order and mesh ratio has been explicitly calculated. Sufficient conditions for uniform convergence are then easily obtained.