A general framework for the construction of piecewise-polynomial local interpolants of minimum degree

作者：Antonelli Michele; Beccari Carolina Vittoria^*; Casciola Giulio

来源：Advances in Computational Mathematics, 2014, 40(4): 945-976.

DOI：10.1007/s10444-013-9335-y

• Spline
• Local interpolation
• Non-uniform knot partition
• Minimum degree
• Design parameters

In this paper we consider the problem of designing piecewise polynomial local interpolants of non-uniformly spaced data. We provide a constructive approach that, for any assigned degree of polynomial reproduction, continuity order, and support width, allows for generating the fundamental spline functions of minimum degree having the desired properties. Finally, the proposed construction is extended to handle open sets of data and to the case of multiple knots.

• 出版日期2014-8