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1、计算方法上机实验报告上课时间：2014-2015 学年秋学期，614 周一拉格朗日插值-1二牛顿插值-3三改进欧拉法-5四四阶龙格-库塔-7五牛顿迭代-96复化 Simpson 公式-11七Romberg 算法-14八. Seidel 迭代法-17九. Gauss 列主元消去法 -20一.拉格朗日插值1.程序代码#includevoid Lagrange()int i=0;double a10,b10,L,L1,L2,L3,L4,x;coutai;coutbi;coutx;L1=(x-a1)*(x-a2)*(x-a3)*b0/(a0-a1)/(a0-a2)/(a0-a3);L2=(x-a0)*
2、(x-a2)*(x-a3)*b1/(a1-a0)/(a1-a2)/(a1-a3);L3=(x-a0)*(x-a1)*(x-a3)*b2/(a2-a0)/(a2-a1)/(a2-a3);L4=(x-a0)*(x-a1)*(x-a2)*b3/(a3-a0)/(a3-a1)/(a3-a2);L=L1+L2+L3+L4;cout#includevoid main()int n,i,j;double A5050,*x,*y;coutn;x=new doublen;y=new doublen;coutxiyi;double K=1,xx,N=0,P;for(i=0;ixx;for(i=0;i#includ
3、edouble fun(double x,double y)return(-0.9*y/(1+2*x);void main()double a,b,*y,h,*x,yp,yc;int n,k;coutab;couth;coutn;y=new doublen;x=new doublen;couty0;x0=a;for(k=0;k#includedouble fun(double x,double y)return(x-y);void main()double a,b,*y,h,x,k1,k2,k3,k4;int n,k;coutab;couth;coutn;y=new doublen;couty
4、0;x=a;cout#includeusing namespace std;double newtondiedai(double a,double b,double c,double d,double x);int main()double a,b,c,d;double x=1.5;coutabcd;x=newtondiedai(a,b,c,d,x);cout0.000001)x=x-(a*x*x*x+b*x*x+c*x+d)/(3*a*x*x+2*b*x+c);return x;2.例子3.运行结果六复化 Simpson 公式1.程序代码（C+ 代码）#include#includedoub
5、le function1(double x)/被积函数double s;s=x/(4+x*x);return s;double function2(double x)/被积函数double s;s=sqrt(x);return s;double ReiterationOfSimpson(double a,double b,double n,double f(double x)/复化 Simpson 公式double h,fa,fb,xk,xj;h=(b-a)/n;fa=f(a);fb=f(b);double s1=0.0;double s2=0.0;for(int k=1;ka;coutb;c
6、outn;cout#includeusing namespace std;#define f(x) (4/(1+x*x) #define epsilon 0.0001 #define MAXREPT 10 double Romberg(double aa,double bb) int m,n;double h,x;double s,q;double ep;double *y =new doubleMAXREPT;double p;h=bb-aa;y0=h*(f(aa)+f(bb)/2.0;m=1;n=1;ep=epsilon+1.0;while(ep=epsilon)&(mab;cout# i
7、nclude # define max 100# define EPS 1e-6float a33=10,-1,-2,-1,10,-2,-1,-1,5;float b3=7.2,8.3,4.2;float x3=0,0,0;float y3;float S(int m)int n;float S=0;float y;for(n=0;nEPS)F=1;printf(%dn,k);while(F=1)printf(迭代次数:%dn,k);for(i=0;i#include#include #define max_dimension 20int n;static float amax_dimensi
8、onmax_dimension;static float bmax_dimension;static float xmax_dimension;void main()int i;int j;int d;int row;float temp;float known_items;float lmax_dimensionmax_dimension;printf(请输入阶数:);scanf(%d,printf(n);printf(请输入系数矩阵的值: );printf(n);for(i=0; ifabs(arowd)row=i;if(row!=d)for(j=d; j-1; i-)known_items=0;for(j=1; jn-i; j+)known_items=known_items+aii+j*xi+j;xi=(bi-known_items)/aii;printf(方程组的根为:nn);for(i=0; in; i+)printf(%.5f ,xi);printf(nn);getch();2.例子3.运行结果
