五种插值法的比较毕业论文.doc

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本科生毕业论文（设计）
题目： 五种插值法的比较
系 部 数学系
学科门类 理学
专 业 数学与应用数学
学 号
姓 名
指导教师

2012 年 X 月 X 日
五种插值法的比较
摘 要
插值法是数值计算中一种重要的方法，在实际生活中有很多函数我们是求不出来的，但我们可以通过该函数在有限点处的取值，用某一函数来逼近它，，到现代用于工程计算、，这篇文章主要介绍了一般常用的五种插值法，，通过它们的定义在形式上的差异来做简单比较；再结合相应的例题归纳总结五种插值法的特点，使我们清楚的知道哪种类型的插值法更适合解决哪一种类型的问题；最后通过实际应用来分析比较Lagrange 插值、Newton插值、三次样条插值和分段插值各自在解决相应问题之间的差异.
关键词：多项式； 插值函数；插值法
ABSTRACT
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Interpolation method is an important method of numerical calculation. In real life, there are many functions that we cannot work out, but we can pass through the function in the finite point value, with a function to approach it, and then estimate the function in other points on the function value. In ancient times have used two equidistant interpolation in astronomical calculations, and applied it in engineering computation, algorithm theory etc in morden time. Interpolation method has many kinds, this article mainly introduces the commonly used five kinds of interpolation, and discuss the difference of five kinds of interpolation method in the theory and application in paper starts from the definition of five kinds of interpolation, by their definitions in the form of difference to do simple comparison，combined with the corresponding examples summarizes five kinds of interpolation features, so that we know which type of interpolation method is more suitable to solve certian kind of problem，and finally by practical application, we can analysis and comparison the differences between Newton Lagrange interpolation, interpolation, three times spline interpolation and piecewise interpolation respectively in the solution of the corresponding problem .