全区间内langrange插值.txt

全区间内Lagrange三点插值

#include "stdio.h"
double nlgr(x,y,n,t)
  int n;
  double t,x[],y[];
  { int i,j,k,m;
    double z,s;
    z=0.0;
    if (n<1) return(z);
    if (n==1) { z=y[0];return(z);}
    if (n==2)
      { z=(y[0]*(t-x[1])-y[1]*(t-x[0]))/(x[0]-x[1]);
        return(z);
      }
    i=0;
    while ((x[i]<t)&&(i<n)) i=i+1;/*为了避免出现高次插值的不稳定性，最多取八点进行插值*/
    k=i-4;
    if (k<0) k=0;
    m=i+3;
    if (m>n-1) m=n-1;
    for (i=k;i<=m;i++)
      { s=1.0;
        for (j=k;j<=m;j++)
          if (j!=i) s=s*(t-x[j])/(x[i]-x[j]);
        z=z+s*y[i];
      }
    return(z);
  }


  main()
  { double t,z;
    static double x[10]={0.10,0.15,0.25,0.40,0.50,
                         0.57,0.70,0.85,0.93,1.00};
    static double y[10]={0.904837,0.860708,0.778801,0.670320,0.606531,
                       0.565525,0.496585,0.427415,0.394554,0.367879};
    t=0.63; z=nlgr(x,y,10,t);
    printf("\n");
    printf("t=%6.3f,   z=%e\n",t,z);
    printf("\n");
  }