牛顿插值.cpp

利用C语言编写的一些常见的差值程序

#include<stdio.h>
#define MAX_N 20
typedef struct tagPOINT 
{double x;
 double y;
}POINT;
int main()
{int n;
 int i,j;
  POINT points[MAX_N+1];double diff[MAX_N+1];
  double x,tmp,newton;
  printf("\nInput n value:");
  scanf("%d",&n);
  if(n>MAX_N)
  {
   printf("The input n is lager than MAX_N,please redefine the MAX_N.\n");
   return 1;
  }
  if(n<=0)
  {
   printf("PLease input a number between 1 and %d.\n",MAX_N);
   return 1;
  }
  printf("Now input the (x_i,y_i),i=0,...,%d:\n",n);
  for(i=0;i<=n;i++)
 	   scanf("%lf%lf",&points[i].x,&points[i].y);
  printf("Now input the x value:\n");
  scanf("%lf",&x);
  for(i=0;i<=n;i++) diff[i]=points[i].y;
  for(i=0;i<=n;i++)
  {
    for(j=n;j>i;j--)
    {
     diff[j]=(diff[j]-diff[j-1])/(points[j].x-points[j-1-i].x);   
    }
  }
  tmp=1;newton=diff[0];
  for(i=0;i<n;i++)
  {
   tmp=tmp*(x-points[i].x);
   newton=newton+tmp*diff[i+1];
  }
   printf("newton(%lf)=%lf\n",x,newton);
   return 0;
}