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Abstract
The characterization of the monotone interpolation and smoothing splines is considered by means of a general optimization problem on a convex subset of a Hilbert space. The results of Hornung [1] and Utreras [2] about the special form of the monotone cubic splines for q = 2 are extended to a higher dimension: it is shown that if q = 3 the solutions of the monotone smoothing problem and the monotone interpolation problem are both polynomial splines of degree 5 with a finite number of knots.