NEWTON'S FORWORD INTERPOLATION METHOD IN C LANGUAGE
Newton Forward.Interpolation is the technique of estimating the value of a function for any intermediate value of the independent variable, while the process of computing the value of the function outside the given range is called extrapolation.
//this method is for 5 elements
#include <stdio.h>
#include <stdlib.h>
int main()
{
int i,x[10],y[10],temp[10],temp1[10],temp2[10],temp3[10],m,y0,y1,y2,y3;
float o, w,u,p,a,h;
int m=4;
printf("enter the elemets of x");
for(i=0;i<=m;i++)
{
scanf("%d",&x[i]);
}
printf("enter the elements of y");
for(i=0;i<=m;i++)
{
scanf("%d",&y[i]);
}
printf("\n first difference");
for(i=0;i<=m-1;i++)
{
temp[i]=y[i+1]-y[i];
printf("\n%d",temp[i]);
if(i==0)
{
y0=temp[i];
printf("\nthe last element =%d",y0);
}
}
printf("\nsecond difference");
for(i=0;i<=m-2;i++)
{
temp1[i]=temp[i+1]-temp[i];
printf("\n%d",temp1[i]);
if(i==0)
{
y1=temp1[i];
printf("\nthe last element of 2nd differnce =%d",y1);
}
}
printf("\n3rd difference ");
for(i=0;i<=m-3;i++)
{
temp2[i]=temp1[i+1]-temp1[i];
printf("\n%d",temp2[i]);
if(i==0)
{
y2=temp2[i];
printf("\nthe last element =%d",y2);
}
}
printf("\n 4th differnce :-");
for(i=0;i<=m-4;i++)
{
temp3[i]=temp2[i+1]-temp2[i];
printf("\n%d",temp3[i]);
if(i==0)
{
y3=temp3[i];
printf("\nthe last element=%d",y3);
}
}
printf("\n enter the value of x");
scanf("%f",&p);
printf("\n enter the value of a and h");
scanf("%f%f",&a,&h);//WHERE a is the first value
u=(p-a)/h;
printf("\n u=%f",u);
printf("enter the vlaue of y0 ");
scanf("%f",&o);
printf("\n the final answer is");
w=o+(u*y0)+(u*(u-1)*y1)/2+(u*(u-1)*(u-2)*y2)/6+(u*(u-1)*(u-2)*(u-3)*y3)/24;//newton forward formula
printf("\n w=%f",w);
return 0;
}
Output:
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