C语言实现的10个关键算法源代码实例

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 转帖
 
推荐人：WD
 

 
1.拉格朗日插值多项式 ，用于离散数据的拟合 

C/C++ code#include <stdio.h>
   #include <conio.h>
   #include <alloc.h>
   float lagrange(float *x,float *y,float xx,int n)      /*拉格朗日插值算法*/
   { int i,j;
     float *a,yy=0.0;     /*a作为临时变量，记录拉格朗日插值多项式*/
     a=(float *)malloc(n*sizeof(float));
     for(i=0;i<=n-1;i++)
     { a[i]=y[i];
       for(j=0;j<=n-1;j++)
       if(j!=i) a[i]*=(xx-x[j])/(x[i]-x[j]);
       yy+=a[i];
     }
   free(a);
   return yy;
}
main()
{ int i,n;
   float x[20],y[20],xx,yy;
   printf("Input n:");
   scanf("%d",&n);
   if(n>=20) {printf("Error!The value of n must in (0,20)."); getch();return 1;}

   if(n<=0) {printf("Error! The value of n must in (0,20)."); getch(); return 1;}
   for(i=0;i<=n-1;i++)
   { printf("x[%d]:",i);
      scanf("%f",&x[i]);
   }
   printf("\n");
   for(i=0;i<=n-1;i++)
   { printf("y[%d]:",i);scanf("%f",&y[i]);}
   printf("\n");
   printf("Input xx:");
   scanf("%f",&xx);
   yy=lagrange(x,y,xx,n);
   printf("x=%f,y=%f\n",xx,yy);
   getch();
}


2.牛顿插值多项式，用于离散数据的拟合 

C/C++ code#include <stdio.h>
#include <conio.h>
#include <alloc.h>
void difference(float *x,float *y,int n)
{ float *f;
   int k,i;
   f=(float *)malloc(n*sizeof(float));
   for(k=1;k<=n;k++)
   { f[0]=y[k];
      for(i=0;i<k;i++)
        f[i+1]=(f[i]-y[i])/(x[k]-x[i]);