Periodic Spline Interpolation with Shifted Nodes Original Research Article

Interpolation problems with periodic splines of defect 2 on an equidistant lattice with two shifted interpolation nodes in each knot interval are considered. Then the periodic Hermite-spline interpolation problem is obtained as a special case. Using generalized Euler-Frobenius polynomials and exponential Euler splines, a simple criterion for the existence and uniqueness of solutions of the considered interpolation problem can be given. This solves an old open problem and generalizes the well-known result on periodic Lagrange-spline interpolation obtained by G. Meinardus, G. Merz, and H. ter Morsche. An extension to cardinal spline interpolation is also described.