三角网格上基于Lebesgue常数最小的混合有理插值

Minimal Lebesgue Constant Blending Rational Interpolation over Triangular Grids

重心有理插值与Thiele型连分式插值相比,具有数值稳定性好、计算量小、有任意高的逼近阶等优点。同时,通过选择适当的权可以使得重心有理插值无极点、无不可达点。基于重心有理插值和牛顿多项式插值,本文构造了上三角网格上的重心-牛顿二元混合有理插值。利用Lebesgue常数最小为目标函数建立了优化模型并求得了最优插值权。数值实例表明了新方法的效力。

Barycentric rational interpolation has various advantages in comparison with Thiele-type continued fraction,such as good numerical stability,small calculation and arbitrarily high approximation order.At the same time,barycentric rational interpolant have no poles and no unattainable points based on those chosen weights.In this paper,the bivariate barycentric-Newton blending rational interpolant is constructed based on the right triangular grid.The optimal model is established by minimizing the Lebesgue constant and the optimal weights are obtained by solving the optimal model.Numerical example is given to show the effectiveness of the new method.