On the construction of optimal monotone cubic spline interpolations (Q1283895)

The authors derive the necessary optimality conditions for an interpolatory spline function minimizing the Holladay approximation of the energy functional. This spline stays monotone if the given interpolation data are monotone. There is applied optimal control theory for state-restricted optimal control problems. The necessary conditions characterize the optimal spline. For the case of two or three interpolation knots (called the local base), the optimality conditions can be treated analytically. The problem can be reduced to polynomial equations which can be solved very easily numerically. The Newton's method can be used for a construction of a numerical algorithm for the optimal monotone spline in the general case. There are given some numerical examples.