nbi.cpp

newton backward interpolation algorithm.

#include<stdio.h>
#include<conio.h>
main()
{
 int n,i,j,m;
 float y[20],x[20][20],p,xv,yv,s;
 printf("How many values do u want:");
 scanf("%d",&n);
 for(i=0;i<n;i++)
 {
   printf("Enter x[%d],y[%d]",i+1,i+1);
 	scanf("%f%f",&y[i],&x[i][0]);
 }
 for(i=1;i<n;i++)
 {
 	for(j=i;j<n;j++)
   {
   	x[j][i]=x[j][i-1]-x[j-1][i-1];
   }
 }
 for(i=0;i<n;i++)
 {
 	for(j=0;j<n;j++)
   {
      if(i<j)
      printf(" \t");
      else
    	printf("%f\t",x[i][j]);
   }
   printf("\n");
 }
 label:
m=1;
printf("\n\nEnter the value of x");
scanf("%f",&xv);
p=(xv-x[n-1][0])/(x[1][0]-x[0][0]);
yv=y[n-1]+p*x[n-1][1];
s=p*(p+1);
for(i=2;i<n;i++)
{
m=m*i;
yv=yv+x[n-1][i]*s/m;
s=s*(p+i);
}
printf("The value of y is %f",yv);
printf("\n\nDo you want to give a new value of x(y/n):");
if(getch()=='y')
goto label;
}