CARDINAL HERMITE SPLINE INTERPOLATION WITH SHIFTED NODES

Generalized cardinal Hermite spline interpolation is considered. A spe cial case of this problem is the classical cardinal Hermite spline int erpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be giv en. 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 applica ble to computing the periodic Hermite spline interpolant. In both case s we only use necessary and sufficient conditions for the existence an d uniqueness of the corresponding Hermite spline interpolant.