基于Lebesgue常数最小的最优保形重心有理Hermite插值

Shape Preserving of Barycentric Rational Hermite Interpolation Basis on the Lebesgue Constant Minimizing

和传统的有理Hermite插值方法相比,重心形式的有理Hermite插值具有许多优点,如计算量小、具有好的数值稳定性、没有极点及不可达点等。进一步研究最优保形重心有理Hermite插值方法。以插值权为决策变量、以Lebesgue常数最小为目标函数、以保形、没有极点及不可达点等为约束条件,建立优化模型求解最优插值权。给出的数值实例表明新方法的有效性。

The barycentric rational Hermite interpolation possess various advantages in comparison with classical rational Hermite interpolants,for example,barycentric rational Hermite interpolants have small amount of calculation,good numerical stability,no poles and no unattainable points,regardless of the distribution of the points.The new shape preserving barycentric rational Hermite interpolation is presented,which with proper weights have no poles and no unattainable points.It is the key issue how to choose weights so that the interpolant with the minimum Lebesgue constant is obtained.The optimal interpolation weights are obtained based on an optimization model.Numerical examples are given to show the effectiveness of the new method.