AI 中文总结
提出一种基于任意解析权函数的重心有理插值展开法，可精确表示解析函数并给出误差，以余弦和第一类贝塞尔函数验证了精度与收敛性。
AI 中文摘要
我们提出了一种利用重心有理插值展开解析函数的方法，其中任意解析权函数定义了插值及节点。截断这些展开式可得到逐次逼近，而展开式的推导过程顺带给出了逼近误差。我们以余弦函数和第一类贝塞尔函数为例，针对多种权函数选择演示了该方法，并考察了逼近插值的精度与收敛性如何随权函数及插值所用节点数变化。
英文摘要
We derive a method of analytic function expansion using barycentric rational interpolation, in which an arbitrary analytic weight function defines the interpolation and nodes. Truncating these expansions yields successive approximations, and the derivation of the expansions gives the approximation error as a byproduct. We demonstrate the method with cosine and the Bessel functions of the first kind for several choices of weight functions, and we examine the accuracy and convergence of the approximate interpolations as a function of the weight and the number of nodes used in the interpolation.
Comments26 main paper pages + 12 appendix pages, 8 figures
