Modelling Reduced Sparse Data

In this paper we discuss the issue of fitting sparse reduced data, where only an ordered collection
of interpolation points in arbitrary euclidean space is given without associated interpolation knots.
The problem is to select the unknown knots which optimize certain cost function measuring the energy of
the fitting curve (a spline) which interpolates reduced data.
The resulting optimization yields a highly non-linear problem and represents a non-trivial task in terms of
setting a computational scheme and in terms of theoretical analysis. In this paper we discuss certain related issues to the above mentioned problem and show some illustrative examples.