超球面上的切触有理插值

Osculatory Rational Interpolation on the Hypersphere

给定单位超球面Sd-1上n+1个点及其对应的参数值和其中n个点处的导向量,基于向量的Samelson逆,构造了广义逆向量值有理函数.证明了所构造的向量值有理函数为[2n,2n]型,在指定的参数值处插值于所给点及其导向量,且向量值有理函数位于超球面上.为了说明方法的有效性,给出了数值实例.

We have created the generalized inverse vector-valued rational function,based on vector＇s Samelson inverse when given n＋1points and nderivative vectors on a unit hypersphere Sd-1.We prove that every vector-valued rational function created is a[2n,2n]type and is on a hypersphere,and the given parameter values interpolate in the given points and its derivative vectors.Numerical results are given to prove the effectiveness of the method.