10个重要的算法C语言实现源代码：拉格朗日，牛顿插值，高斯，龙贝格，牛顿迭代，牛顿-科特斯，雅克比，秦九昭，幂法，高斯塞德尔

6.牛顿-科特斯求积公式，求定积分

C/C++ code

<!--code highlighting produced by actipro codehighlighter (freeware)http://www.codehighlighter.com/-->#include<stdio.h>#include<math.h>int NC(a,h,n,r,f)float (*a)[];float h;int n,f;float *r;{ int nn,i; float ds; if(n>1000||n<2) { if (f)   printf("\n Faild! Check if 1<n<1000!\n",n);   return(-1);}if(n==2){ *r=0.5*((*a)[0]+(*a)[1])*(h);return(0);}if (n-4==0) { *r=0;*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]);return(0);}if(n/2-(n-1)/2<=0)nn=n;elsenn=n-3;ds=(*a)[0]-(*a)[nn-1];for(i=2;i<=nn;i=i+2)ds=ds+4*(*a)[i-1]+2*(*a)[i];*r=ds*(h)/3;if(n>nn)*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]);return(0);}main(){ float h,r; int n,ntf,f; int i; float a[16];printf("Input the x[i](16):\n"); for(i=0;i<=15;i++) scanf("%d",&a[i]);h=0.2;f=0;ntf=NC(a,h,n,&r,f);if(ntf==0) printf("\nR=%f\n",r);  else printf("\n Wrong!Return code=%d\n",ntf);  getch();}

7.雅克比迭代，求解方程近似解

C/C++ code

<!--code highlighting produced by actipro codehighlighter (freeware)http://www.codehighlighter.com/-->#include <stdio.h>#include <math.h>#define N 20#define MAX 100#define e 0.00001int main(){ int n; int i,j,k; float t; float a[N][N],b[N][N],c[N],g[N],x[N],h[N]; printf("\nInput dim of n:");   scanf("%d",&n); if(n>N) { printf("Faild! Check if 0<n<N!\n"); getch(); return 1; } if(n<=0) {printf("Faild! Check if 0<n<N!\n"); getch(); return 1;} printf("Input a[i,j],i,j=0…%d:\n",n-1); for(i=0;i<n;i++)   for(j=0;j<n;j++)   scanf("%f",&a[i][j]); printf("Input c[i],i=0…%d:\n",n-1); for(i=0;i<n;i++)scanf("%f",&c[i]); for(i=0;i<n;i++)   for(j=0;j<n;j++)   { b[i][j]=-a[i][j]/a[i][i];   g[i]=c[i]/a[i][i]; }  for(i=0;i<MAX;i++)   { for(j=0;j<n;j++)     h[j]=g[j];     { for(k=0;k<n;k++)       { if(j==k) continue; h[j]+=b[j][k]*x[k]; }     }     t=0;     for(j=0;j<n;j++)     if(t<fabs(h[j]-x[j])) t=fabs(h[j]-x[j]);     for(j=0;j<n;j++)     x[j]=h[j];     if(t<e)     { printf("x_i=\n");       for(i=0;i<n;i++)     printf("x[%d]=%f\n",i,x[i]);       getch();       return 0;     }     printf("after %d repeat , return\n",MAX);     getch();     return 1;   }   getch();}

8.秦九昭算法

C/C++ code

<!--code highlighting produced by actipro codehighlighter (freeware)http://www.codehighlighter.com/-->#include <math.h>float qin(float a[],int n,float x){    float r=0;    int i;    for(i=n;i>=0;i--)    r=r*x+a[i];    return r;}main(){    float a[50],x,r=0;    int n,i;    do    {    printf("Input frequency:");        scanf("%d",&n);    }    while(n<1);    printf("Input value:");    for(i=0;i<=n;i++)    scanf("%f",&a[i]);    printf("Input frequency:");    scanf("%f",&x);    r=qin(a,n,x);    printf("Answer:%f",r);    getch();}

9.幂法

C/C++ code

<!--code highlighting produced by actipro codehighlighter (freeware)http://www.codehighlighter.com/-->#include<stdio.h>#include<math.h>#define N 100#define e 0.00001#define n 3float x[n]={0,0,1};float a[n][n]={{2,3,2},{10,3,4},{3,6,1}};float y[n];main(){ int i,j,k;   float xm,oxm;   oxm=0;   for(k=0;k<N;k++)   { for(j=0;j<n;j++)      { y[j]=0;        for(i=0;i<n;i++)        y[j]+=a[j][i]*x[i];      }      xm=0;      for(j=0;j<n;j++)      if(fabs(y[j])>xm) xm=fabs(y[j]);      for(j=0;j<n;j++)      y[j]/=xm;      for(j=0;j<n;j++)      x[j]=y[j];      if(fabs(xm-oxm)<e)      { printf("max:%f\n\n",xm);       printf("v[i]:\n");        for(k=0;k<n;k++) printf("%f\n",y[k]);       break;      }      oxm=xm;    } getch();}

10.高斯塞德尔

C/C++ code

<!--code highlighting produced by actipro codehighlighter (freeware)http://www.codehighlighter.com/-->#include<math.h>#include<stdio.h>#define N 20#define M 99float a[N][N];float b[N];int main(){    int i,j,k,n;    float sum,no,d,s,x[N];    printf("\nInput dim of n:"); scanf("%d",&n); if(n>N) { printf("Faild! Check if 0<n<N!\n "); getch();   return 1; } if(n<=0) { printf("Faild! Check if 0<n<N!\n ");getch();return 1;} printf("Input a[i,j],i,j=0…%d:\n",n-1); for(i=0;i<n;i++) for(j=0;j<n;j++) scanf("%f",&a[i][j]); printf("Input b[i],i=0…%d:\n",n-1); for(i=0;i<n;i++) scanf("%f",&b[i]);    for(i=0;i<n;i++) x[i]=0; k=0; printf("\nk=%dx=",k); for(i=0;i<n;i++) printf("%12.8f",x[i]); do { k++;     if(k>M){printf("\nError!\n”);getch();}     break; } no=0.0; for(i=0;i<n;i++)  { s=x[i];    sum=0.0;    for(j=0;j<n;j++)    if (j!=i) sum=sum+a[i][j]*x[j];    x[i]=(b[i]-sum)/a[i][i];    d=fabs(x[i]-s);    if (no<d) no=d; } printf("\nk=%2dx=",k); for(i=0;i<n;i++)   printf("%f",x[i]);}while (no>=0.1e-6);if(no<0.1e-6){ printf("\n\n answer=\n");  printf("\nk=%d",k);  for (i=0;i<n;i++)  printf("\n x[%d]=%12.8f",i,x[i]);}getch();} 

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