A local algorithm for constructing non-negative cubic splines
The authors describe an algorithm for interpolation of positive functions by non-negative splines. The algorithm can be described shortly as follows: First they consider the natural cubic spline which satisfies the interpolation conditions. In the second step in each subinterval between two successive knots in which this spline assumes negative values, the relevant portion of the spline is replaced by a non-negative cubic spline. This is carried out by the addition of extra knots, the location of which depends only on the values of the original spline. In the last step these additional knots are varied in order to minimize the strain energy integral. The described algorithm can be applied also to produce splines which stay locally (i.e. between two consecutive knots) below or above given constant bounds.
scientific article; zbMATH DE number 4208739
scientific article