数值分析课程上机作业计算报告
班 级：
学 号： 姓 名：
专 业：大地测量学及测绘工程
指导老师： 联系电话：
数值分析上机实验报告
序 言
通过数值分析的理论知识的学习，此次实验将我们学过的理论知识运用于实践之中。本次实验，我选用的计算机语言为MATLAB，其主要有一下几个特点。 1．编程效率高
MATLAB是一种面向科学与工程计算的高级语言，允许使用数学形式的语言编写程序，且比BASIC、FORTRAN和C等语言更加接近我们书写计算公式的思维方式，用MATLAB编写程序犹如在演算纸上排列出公式与求解问题。因此，MATLAB语言也可通俗地称为演算纸式科学算法语言。由于它编写简单，所以编程效率高，易学易懂 2. 用户使用方便
MATLAB语言与其他语言相比，较好的解决了上述问题，把编辑、编译、链接和执行融为一体。它能在同一画面上进行灵活操作，快速排除输入程序中的书写错误、语法错误以至语义错误，从而加快了用户编写、修改和调试程序的速度，可以说在编程和调试过程中它是一种比VB还要简单的语言。 3. 方便的绘图功能
MATLAB的绘图是十分方便的，它有一系列绘图函数（命令），例如线性坐标、对数坐标、半对数坐标及极坐标，均只需调用不同的绘图函数（命令），在图上标出图题、XY轴标注，格（栅）绘制也只需调用相应的命令，简单易行。另外，在调用绘图函数时调整自变量可绘出不变颜色的点、线、复线或多重线。这种为科学研究着想的设计是通用的编程语言所不能及的。
数值分析上机实验报告
目 录
1.实验一 ······················································································································· 1
1.1题目 ··················································································································· 1 1.2计算思路 ··········································································································· 1 1.3计算结果 ··········································································································· 1 1.4总结 ··················································································································· 6 2.第二题 ······················································································································· 7
2.1题目 ··················································································································· 7 2.2 松弛思想分析 ·································································································· 7 2.3问题的求解 ······································································································· 7 2.4总结 ················································································································· 10 3.第三题 ····················································································································· 11
3.1题目 ················································································································· 11 3.2 Runge-Kutta法的基本思想 ··········································································· 11 3.3 问题的求解 ···································································································· 11 3.4问题的总结 ····································································································· 14 总结······························································································································ 15 附件······························································································································ 16
实验一程序设计 ··································································································· 16 实验二程序设计 ··································································································· 16 实验三程序设计 ··································································································· 17
数值分析上机实验报告
实验一：插值问题
1.1题目
已知：a=-5,b=5, 以下是某函数 f(x)的一些点（xk,yk）, 其中xk=a+0.1(k-1) ,k=1,..,101；（数据略）。
请用插值类方法给出函数f(x)的一个解决方案和具体结果。并通过实验考虑下列问题：
（1）Ln(x)的次数n越高，逼近f(x)的程度越好？ （2）高次插值收敛性如何？
（3）如何选择等距插值多项式次数 ？
（4）若要精度增高，你有什么想法？ 比如一定用插值吗？ （5）逼近某个函数不用插值方式，有何变通之举？ （6）函数之间的误差如何度量，逼近的标准又是什么？ (7) 如何比较好的使用插值多项式呢？
1.2计算思路
本题我选用拉格朗日插值函数，拉格朗日插值函数的构建算法是从101组数据中等距选取n组数据来构造n阶的拉格朗日插值函数，然后在[-5,5]区间选取m个插值点带入插值多项式计算出m组（x,y），本题中，我分别取了n=6,8,10，20四种不同的阶数，然后利用matlab绘图命令查看插值函数图像与原函数图像的逼近效果。
1
