【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。更多还原

【Abstract】 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.更多还原