The derivation of cubic splines with obstacles by methods of optimization and optimal control (Q1093113)

Interpolating splines which are restricted in their movement by the presence of obstacles are investigated. For simplicity we mainly treat cubic splines which are required to be nonnegative. The extension to splines of higher order and to certain other forms of obstacles is straightforward. Methods of optimization and of optimal control are used to obtain necessary optimality criteria. These criteria are applied to derive an algorithm to compute splines which are restricted to constant lower or upper bounds. There is a numerical example which illustrates the method presented.