基于差商的插值法拓展思路与教学方法研究  

Idea of Expanding the Interpolation ExtensionBased on the Divided Difference

作　　者：邹乐[1] 吴志泽 谢进[1] 檀明[1] 王晓峰 Zou Le;Wu Zhize;Xie Jin;Tan Ming;Wang Xiaofeng(School of Artificial Intelligence and Big Data,Hefei University,Hefei,Anhui 230601,China)

机构地区：[1]合肥学院人工智能与大数据学院,安徽合肥230601

出　　处：《黑龙江工业学院学报（综合版）》2021年第5期13-21,共9页Journal of Heilongjiang University of Technology(Comprehensive Edition)

基　　金：国家级新工科研究与实践项目“应用型高校新工科专业‘模块化课程池’建设的实践研究”(项目编号:E-ZYJG20200225);安徽省重大教学研究项目“融合现代产业学院和模块池的计算机类新工科人才培养模式研究与实践”(项目编号:2020jyxm1594);安徽省线上教学示范高校项目“省级线上教学示范高校”(项目编号:2020xssfgx14);安徽省质量工程项目“软件技术系列课程教学团队”(项目编号:2019jxtd096);合肥学院重大教学改革研究项目“融合模块池和产业学院的新工科人才培养模式的研究”(项目编号:2019hfjyxm01)。

摘　　要：插值法是函数逼近的一种重要方法,也是计算方法课程中的重点和难点。拟对Newton插值多项式进行多种拓展研究和分析,结合差商插值法的特点,研讨基于差商的Newton插值与基于反差商的Thiele型连分式插值,参数化Newton型插值多项式和参数化连分式插值等几种插值方法的内在关系。构造过程展示了如何利用构造法思想拓展差商表和差商公式,进而培养学生的科研探索与创新思维,提高学生解决实际问题的能力。Interpolation is an important method of function approximation,and it is also a key and difficult point in the computation course.Considering the characteristics of the interpolation method based on divided difference,we conduct a variety of extended research and analysis of the Newton interpolation polynomial,and use the construction method is used to study the internal relations of the Newton interpolation,the Thiele type continued fraction interpolation based on the inverse difference,the parameterized Thiele type continued fraction interpolation and the parameterized Newton type interpolation polynomial.With this,the construction process demonstrates how to use the ideas of the construction method to expand the divided difference table and the divided difference formula,thus cultivate students'research exploration and innovative thinking,and improve students'ability to solve practical problems.

关 键 词：差商 反差商 虚拟节点 连分式 参数化连分式 

分 类 号：G642.0[文化科学—高等教育学] O241.3[文化科学—教育学]