This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform 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 non-uniform case, and to complete families of arbitrary support width. Furthermore it provides new local interpolating polynomial splines with prescribed smoothness and polynomial reproduction properties.
C.V. Beccari, G.Casciola, L.Romani (2013). Construction and characterization of non-uniform local interpolating polynomial splines. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 240, 5-19 [10.1016/j.cam.2012.06.025].
Construction and characterization of non-uniform local interpolating polynomial splines
BECCARI, CAROLINA VITTORIA;CASCIOLA, GIULIO;ROMANI, LUCIA
2013
Abstract
This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform 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 non-uniform case, and to complete families of arbitrary support width. Furthermore it provides new local interpolating polynomial splines with prescribed smoothness and polynomial reproduction properties.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.