Error optimization in the operators of interlineation of functions on \(M\) parallel lines (Q2044002)

A Hermite-type approximation problem is considered in this article, where particular attention is paid on the optimisation of the parameters that occur in the method. The special property which this approximation algorithm provides is that the approximant and the function to be approximated have the same differentialbilty properties which is useful and unusual in other methods (such as splines in one or more dimensions), and also particularly appropriate for the Hermite setting studied in this paper.