Complex Cubic Spline Interpolation I

Abstract

The study of cubic splines and deficient cubic splines interpolating at intermediate points including nodal points was made in [3], [5], [6] and [7]. The complex cubic splines were considered in [1] and [2]. The deficient complex cubic spline function interpolating at the nodal points of subarcs of a rectifiable Jordan are was considered by Chatterjee and Dikshit [4]. In the present paper we consider a natural question whether the deficient complex cubic spline function can be obtained which interpolates at an intermediate point of the subarcs including nodal points. We show that the analysis of the paper [4] can be extended to establish that interpolations at intermediate points are possible.