Cardinal Hermite Spline Interpolation with Shifted Nodes

Abstract

Abstract. Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be given. Furthermore, a new efficient algorithm for the computation of the cardinal Hermite spline interpolant is obtained, which is mainly based on fast Fourier transform. This algorithm is shown to be also applicable to computing the periodic Hermite spline interpolant. In both cases we only use necessary and sufficient conditions for the existence and uniqueness of the corresponding Hermite spline interpolant.