切触有理插值新方法  

A new method of osculatory rational interpolation

作　　者：经慧芹[1] Jing Huiqin(School of Continuing Education, Kunming University of Science and Technology, Kun'ming 650051, China)

机构地区：[1]昆明理工大学成人教育学院,云南昆明650051

出　　处：《纯粹数学与应用数学》2018年第1期15-25,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11461703)

摘　　要：针对传统连分式插值,计算复杂度高,计算过程中分母为零的不可预知性及插值函数不满足某些给定条件,应用不方便等问题,利用已知节点、函数值、导数值,构造两个多项式,分别作为有理插值函数的分子和分母,得出各阶导数条件下切触有理插值的新公式,并给出特殊情形的表达式.若添加适当的参数,可任意降低插值函数次数.该方法计算简洁,应用方便,插值函数的分母在节点处不为零且满足全部插值条件.数值例子验证了新方法的可行性、有效性和实用性.In order to solve the inherent issues with the conventional continued fraction,including complicated operation,attempt to divide by zero,faulty interpolation functions and limited applications,a new method is presented.It creates two polynomials,one as nominator and another as denominator of the rational interpolation function,out of provided nodes,function outputs and derivatives.Both polynomials lead to new formulas of osculatory rational interpolation under derivative of each order and to expressions under special circumstances.With appropriate parameters added,the exponent of interpolation functions can be arbitrarily reduced.This method simplifies operation,expands application,avoids dividing by zero and defies any faulty interpolation functions.a numerical example attests to the method is practicability,efficiency and universality.

关 键 词：切触有理插值 新方法 公式 

分 类 号：O241.3[理学—计算数学]