Smooth functions and local extreme values

The problem of specifying a smooth and simple function that approximates noisy data is considered. A new automatic method is described that is based on solving a constrained optimisation problem. The target functional to be minimised is the sum of the squared residuals penalised by the curve length of the approximation. Multiresolution and monotonicity constraints provide a good approximation to the data with a small number of local extreme values. The new method can also be applied to density estimation.