二元复合重心型混合有理插值

摘要

Barycentric rational interpolant was constructed by Schneider and Werner ,which has small calculation quantity ,good numerical stability in comparison with Thiele‐type continued fraction rational interpolant .Moreover ,poles and unattainable points are prevented when choosing the appropriate weights .In this paper ,the new method of bivariate composite barycentric blending rational interpolation in rectangular domain is studied .Firstly ,bivariate New ton interpolation polynomial is constructed in a small rectangular domain .Then ,bivariate composite barycentric blending rational interpolation is constructed by means of composite barycentric rational interpolation and some interpolation properties are proved ,such as bivariate composite barycentric blending ra‐tional interpolant has no poles and unattainable points .Finally ,a numerical example is given to show the effectiveness of the new method .%Schneider和Werner提出的重心有理插值比T hiele型连分式有理插值计算量小，数值稳定性好，选择适当的权可以不出现极点和不可达点。本文研究矩形域上的二元复合重心型混合有理插值新方法。首先在小矩形域上构造二元New ton插值多项式，然后通过复合重心有理插值，构造出了二元复合重心型混合有理插值，证明了二元复合重心型混合有理插值无极点和不可达点，最后给出的数值例子验证了新方法的有效性。