Resumen de Construction and characterization of non-uniform local interpolating polynomial splines

Carolina Vittoria Beccari, Giulio Casciola, Lucia Romani

• This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on nonuniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are rational, our approach provides spline interpolants having low, and sometimes minimum degree.

  Thanks to its generality, the proposed framework also allows us to recover uniform local interpolating splines previously proposed in the literature, to generalize them to the nonuniform case, and to complete families of arbitrary support width. Furthermore it provides new local interpolating polynomial splines with prescribed smoothness and polynomial reproduction properties.