基于Lebesgue常数最小保水平渐近线的重心有理插值  

Barycentric Rational Interpolation Based on Lebesgue Constant Minimum Level Preserving Asymptote

作　　者：赵前进 杨帆 ZHAO Qianjin;YANG Fan(School of Mathematics and Big Data,Anhui University of Science&Technology,Huainan 232001,Anhui,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：《合肥学院学报（综合版）》2024年第2期28-31,36,共5页Journal of Hefei University：Comprehensive ED

基　　金：国家自然科学基金项目“有理插值新方法及其在三维数字模型信息保护中的应用研究”(60973050);安徽理工大学环境友好材料与职业健康研究院(芜湖)研发专项资金“基于大数据的家庭近视眼防控关键技术及系统研发”(ALW2021YF09)。

摘　　要：提出了一种保水平渐近线的重心有理插值方法。首先研究重心有理插值保水平渐近线的条件,进一步以Lebesgue常数最小为目标函数,同时以重心有理插值函数没有极点、没有不可达点、插值函数保水平渐近线以及重心权的规范化等为约束条件,建立优化模型解得最优权,从而得到保水平渐近线的重心有理插值。通过数值例子证明了算法有效性。In this paper,a barycentric rational interpolation method with horizontal asymptotes is pro⁃posed.Firstly,the condition of level preserving asymptotes is studied for BRI.Secondly,an optimal weights optimization model is constructed by using the minimum Lebesgue constant as the objective function.The constraint conditions of optimization model of the BRI include no pole,no inaccessible point,the interpolation function level preserving asymptotes,and the normalization of barycentric weights.Finally,the barycentric rational interpolation with horizontal-preserving asymptotes is ob⁃tained.The effectiveness of the algorithm is proved by numerical examples.

关 键 词：LEBESGUE常数 重心有理插值 插值权 保水平渐近线 

分 类 号：O241.3[理学—计算数学]