构造给定极点的有理插值新方法  

A New Method for Constructing Rational Interpolation with Prescribed Poles

作　　者：张玉武[1] ZHANG Yuwu(Department of Basic Education of Lu’an Vocational Technical College, Lu’an 237158, China)

机构地区：[1]六安职业技术学院基础部

出　　处：《安庆师范大学学报（自然科学版）》2019年第3期7-9,15,共4页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(60973050);安徽省质量工程重点教学研究项目(2013jyxm335)

摘　　要：根据给定极点得到蕴含极点信息的函数,通过新的插值条件,在插值区间上构造多项式插值函数,并除以蕴含极点信息的函数,最终可以得到一个有理插值函数。新构造的有理函数不但保留了给定极点的信息,在插值区间上避免新的极点产生,而且具有很好的逼近效果。给出的数值实例说明新方法具有构造简单、计算方便的优点。According to the prescribed poles, a function containing pole information is obtained. By using new interpolation conditions, a polynomial interpolation function is constructed on the interpolation interval. Finally, a rational interpolation function is obtained by dividing the polynomial interpolation function by the function containing prescribed poles. The new constructed rational function not only retains the information of the given poles, but also avoids the generation of new poles on the interpolation interval, and has a good approximation effect. The numerical examples show that the new method has the advantages of simple construction and convenient calculation.

关 键 词：计算数学 极点 有理函数 插值 

分 类 号：O24[理学—计算数学]