摘要本文首先通过对常见代数插值法入手研究，主要给出一些常见的代数插值法的定义包括拉格朗日插值、牛顿插值、低次线性插值以及三次样条插，通过列举实例并且用MATLAB绘制函数图像对这几种方法进行比较分析，结果表明对于一些结构比较复杂的函数，Newton插值比Lagrange插值更占优势。拉格朗日插值和牛顿插值虽然满足在节点上的函数值相等，在许多实际问题中函数值相等是最基本的要求，并且要符合相切，而对应的导数值也是要求相等，在特殊的时候高阶导数值相等也是需要的。低次插值和三次样条插值很好的解决了龙格现象，而且三次样条函数插值的图像有更好地光滑度。72334

 其次从几种常见空间插值方法包括反距离加权插值、克里金插值和最近邻点插值入手研究。选取山区高程，运用三种空间插值方法生成DEM模型，并从精度和DEM模型可视化两个角度进行三种空间插值方法的对比。结果表明，克里金插值更适合于山区DEM生成使用中。

 该论文有图12幅，表5个，参考文献21篇。

毕业论文关键词：代数插值  MATLAB  空间插值  比较分析

Comparison and analysis of common interpolation methods

Abstract This paper based on the common algebraic interpolation method o, and mainly presents the definition of some common algebraic interpolation method 。By listing examples and MATLAB drawing function image several methods for the comparative analysis, the results show that for some function of the structure is more complex, and Newton interpolation is more advantage than though Lagrange interpolation。 Though Lagrange interpolation and Newton meeting at the node function values are equal, in many practical problems not only meet the above requirements, but also the corresponding derivative values are equal, or even require higher derivative values are equal。 Low time interpolation and cubic spline interpolation well solve the runge phenomenon, and cubic spline function interpolation image has better smoothness。 

Secondly from several common spatial interpolation methods are include inverse distance weighted interpolation and kriging interpolation and nearest neighbor interpolation points are listed。 Selecting mountain elevation, using three methods of spatial interpolation generate DEM model, and from two angles of precision and DEM model visualization for comparison of three methods of spatial interpolation。 The results show that the kriging interpolation is more suitable for the mountains in DEM generation using。      The paper has 12 figures,5 tables and 21 references。

Key word：algebra interpolation  MATLAB  spatial interpolation  Comparison and analysis

目  录

摘要 I

Abstract II

目  录 III

图清单 IV

表清单 V

变量注释表 V

1 绪论 1

1。1  论文的研究意义 1

1。2  论文的研究思路 2

1。3  论文的研究内容 2

1。4  国内外研究的现状 2

2  常见代数插值方法的基本理论 5

2。1 常见代数插值法的简介 5

2。2  常见代数插值法的比较 8

3。常见空间插值方法的理论基础