This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with additional smoothness at the vertices of the initial partition, and of the lowest possible degree. A normalized B-spline-like representation for the considered spline space is provided. In addition, several quasi-interpolation operators based on blossoming and control polynomials have also been developed. Some numerical tests are presented and compared with some recent works to illustrate the performance of the proposed approach.

翻译：本文研究埃尔米特密切插值样条。针对实区间的一个划分，并在每个子区间等分为两个更小子区间的细化基础上，考虑一个在初始划分顶点处具有额外光滑性且次数尽可能低的光滑样条空间。给出了该样条空间的一种归一化类B样条表示。此外，基于开花方法和控制多项式，还发展了几种拟插值算子。通过数值实验并与近期研究对比，展示了所提方法的性能。