基于上三角域上的形状控制重心混合有理插值  

Shape control in barycentric blending rational interpolation over triangular grids

作　　者：赵前进[1] 朱六三 

机构地区：[1]安徽理工大学理学院,安徽淮南232001

出　　处：《安徽大学学报（自然科学版）》2014年第3期1-5,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60973050);安徽省教育厅自然科学基金资助项目(KJ2009A50)

摘　　要：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.基于上三角域上的重心——牛顿二元混合有理插值,以Lebesgue常数最小为目标函数、偏导数的符号为约束条件建立了优化模型,求得最优插值权.此方法不仅可以插值未知函数而且可以有效对形状作局部控制.数值实例表明了新方法的效果.Barycentric rational interpolation possesses various advantages in comparison with Thieletype continued fraction, such as good numerical stability, small calculation and arbitrarily high approximation order. At the same time, barycentric rational interpolant had no poles and no unattainable points based on those chosen weights. In this paper, the barycentric-Newton blending rational interpolation was constructed based on the right triangular grid. The optimal model was established by minimizing the Lebesgue constant and using partial derivative, the optimal wights were obtained by solving the optimal model. The method could not only do the interpolation to unknown function but also have effective local control of shape. The numerical example was given to show the effectiveness of the new method.

关 键 词：重心有理插值 LEBESGUE常数 偏导数 权 形状控制 

分 类 号：O241[理学—计算数学]