A dual algorithm for convex-concave data smoothing by cubic \(C^ 2\)- splines
The problem of smoothing a given data set by a cubic \(C^ 2\)-spline is discussed. The spline may require to be convex in some parts of the domain and concave in other parts. The special structure of the arising finite dimensional convex program allows a dualization such that the resulting concave dual program is unconstrained. The latter program is treated numerically much more easier than the original program. In this paper the details for applying the strategy to the present smoothing problem are elaborated. Also some numerical tests are presented.
scientific article; zbMATH DE number 4151705