论文标题
在平面多项式几何插值上
On Planar Polynomial Geometric Interpolation
论文作者
论文摘要
在本文中，重新研究了数据点的平面多项式几何插值。简单的足够的几何条件表示插入剂的存在通常得出。他们要求数据点在某些离散意义上成为凸。由于几何插值仅基于已知数据，因此可以将其视为多项式函数插值的参数对应物。已建立的结果证实了Höllig-koch的猜想对存在的任何程度的参数多项式曲线在平面案例中的存在和近似顺序。
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a certain discrete sense. Since the geometric interpolation is based precisely on the known data only, one may consider it as the parametric counterpart to the polynomial function interpolation. The established result confirms the Höllig-Koch conjecture on the existence and the approximation order in the planar case for parametric polynomial curves of any degree stated quite a while ago.
