二元复合重心有理插值

Bivariate Composite Barycentric Rational Interpolation

Thiele型有理插值常被用来逼近带极点的函数,但是它难以避免极点和不可达点,也难以控制极点。重心有理插值方法包含极点和不可达点的信息,通过选择权可避免极点和不可达点。研究矩形域上的二元复合重心有理插值,首先对小矩形域上构造二元重心有理插值,然后基于重心复合方法构造了二元复合重心有理插值,证明了二元复合重心有理插值无极点、不可达点,最后给出的数值例子验证了新方法的逼近效果。

Thiele-type rational interpolation is often used to approximate functions with poles.But it is hard to avoid poles and unattainable points and is hard to control location of poles.The information about poles and unattainable points is included in the barycentric rational interpolant.In this paper,the new method of bivariate composite barycentric rational interpolation in rectangular domain is studied.At first,bivariate barycentric rational interpolation is constructed in a small rectangular domain.Then,bivariate composite barycentric rational interpolation is constructed based on the composite barycentric sheme and some interpolation properties are proved that such as bivariate composite barycentric rational interpolant has no poles and unattainable points.At last,numerical examples are given to show the approximating effectiveness of the new method.