第五版数值分析实验.docx

1、第五版数值分析实验实验一实验题目：编写一个拉格朗日插值函数，对不多于9个点的插值节点都可以求出插值函数，任意给定输入x值都可以求出y值。例如：（0,1）,(1,1) ,(4,2) ,(9,3) ,(16,4) ,(25,5) ,(36,6) ,(49,7) ,(64,8)，这实际上是一个平方根函数随意输入x在0，64上的值都可以输出一个y值。进一步可以在这区间上画出图像。实验原理：方法一 拉格朗日function y = lagranger(x0,y0,x);%UNTITLED Summary of this function goes here% Detailed explanation g

2、oes heren=length(x0);m=length(x);for i=1:m z=x(i); s=0.0; for k=1:n li=1.0; for j=1:n if j=k li=li*(z-x0(j)/(x0(k)-x0(j); end end s=li*y0(k)+s; end y(i)=s; end三.函数使用 斐波那锲函数function f = fib( n )%UNTITLED2 Summary of this function goes here% Detailed explanation goes heref=1 1;if n=1&n0 f=1;else if n=

3、2 f=1 1; else for i=3:n f(i)=f(i-2)+f(i-1); end end end g=f(n); end y=fib(10)y = 1 1 2 3 5 8 13 21 34 55 plot(y, DisplayName, y, YDataSource, y); figure(gcf) 实验二1.编写一个函数实现被积分function y = shiyan2(x)%UNTITLED2 Summary of this function goes here% Detailed explanation goes herey=log(x).*sqrt(x); end 2.使

4、用MATLAB画出函数曲线X=0.01:0.001:1Y=shiyan2(x)Plot(x,y,-b)Grid on3.编写复合梯形公式计算积分函数function y = echelon(h)%UNTITLED Summary of this function goes here% Detailed explanation goes heren=length(h);y=0,0;for i=1:n; temp =0.001; result =0; while temp+h(i)1 x=(shiyan2(temp)+shiyan2(temp+h(i)*h(i)/2; result =result

5、+x; temp =temp+h(i); end result = result +(shiyan2(temp)+shiyan2(1)*h(i)/2; y(i)=result;endend输入一组步长h调用符合梯形积分函数计算积分结果计算积分结果的误差 4.辛普森方法function y = quad(h)%UNTITLED4 Summary of this function goes here% Detailed explanation goes heren=length(h);y=0,0;for i=1:n; temp=0.001; result =0; while temp+h(i)k,t=A(k,:); A(k,:)=A(m,:); A(m,:)=t; end A(k+1):n,(k+1):(n+1)=A(k+1):n,(k+1):(n+1)-A(k+1):n,k)/A(k,k)*A(k,(k+1):(n+1); A(k+1):n,k)=zeros(n-k,1);endx=zeros(n,1);x(n)=A(n,n+1)/A(n,n);for k=n-1:-1:1 x(k,:)=(A(k,n+1)-A(k,(k+1):n)*x(k+1):n)/A(k,k); end