DMBVP for tension splines

This paper addresses a new approach in solving the problem of shape preserving spline interpolation. Based on the formulation of the latter problem as a differential multipoint boundary value problem for hyperbolic and biharmonic tension splines we consider its finite-difference approximation. The resulting system of linear equations can be efficiently solved either by direct (Gaussian elimination) and iterative methods (successive over-relaxation (SOR) method and finite-difference schemes in fractional steps). We consider the basic computational aspects and illustrate the main advantages of this original approach.