复合重心有理插值的保形方法  

Shape preserving method of composite Barycentric rational interpolation

作　　者：马登攀 MA Deng-pan(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第2期208-211,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金项目(60973050);校级重点自然科学研究项目(2022XJZD027).

摘　　要：传统的插值方法存在无法避免极点、不可达点等问题,为了提高有理插值逼近的精确度,考虑重心有理插值的优点,提出了复合重心插值的保形方法.将误差平方和最小作为目标函数,保形条件、没有极点和插值权不为零等作为限制要求,建立插值函数的优化模型,结合LINGO软件,求解出函数最优权值,结果表明插值函数保形方法的可行性.In order to improve the accuracy of rational interpolation,a conformal method of composite barycentric interpolation was proposed considering the advantages of barycentric rational interpolation.The minimum sum of the squares of errors was taken as the objective function,and the conformal condition,no poles and the interpolation weight was not zero were taken as the restriction requirements.The optimization model of the interpolation function was established,and the optimal weight of the function was solved by using LINGO software.The results showed that the conformal method of the interpolation function was feasible.

关 键 词：Padé-type逼近 重心插值 极点 插值权 保形 优化模型 

分 类 号：O241.3[理学—计算数学]