Implementation of Newton Forward Interpolation Formula in C.

Here is the code..

//AIM: TO FIND THE VALUE USING NEWTON FORWARD INTERPOLATION FORMULA

#include<stdio.h>

#define differ(b,a) (b-a)

#define m 5

int fact(int );

void main()

{

float a[m],fx[m][m],t,u,f;

float fxx=0.0,fxx1=1.0,fxx2=0.0;

int i,j;

printf("NEWTON FORWARD INTERPOLATION FORMULA\n");

printf("enter %d values of x\n",m);

for(i=0;i<m;i++)

scanf("%f",&a[i]);

printf("enter %d values of fx\n",m);

for(i=0;i<m;i++)

scanf("%f",&fx[i][0]);

printf("enter the value across which you want to find value\n");

scanf("%f",&t);

for(i=0;i<m;i++)

{

for(j=i;j<m;j++)

{

fx[j+1][i+1] = differ(fx[j+1][i],fx[j][i]);

}

}

printf("TABLE IS\n");

printf("x :\n");

for(i=0;i<m;i++)

printf("%f\t",a[i]);

printf("fx\t\t$fx\t\t$2fx\t\t$3fx\t\t$4fx\n");

for(i=0;i<m;i++)

{

for(j=0;j<m;j++)

{

if(j<=i)

printf("%f\t",fx[i][j]);

else

printf("\t\t");

}

}

u = ((t-a[0])/(a[1]-a[0]));

for(i=0;i<m-1;i++)

{

fxx1=fxx1*(u-i);

fxx2 = fxx2+((fxx1*fx[i+1][i+1])/(fact(i+1)));

}

fxx = fxx2+fx[0][0];

printf("the value of f(t) is: %f\n",fxx);

}

int fact(int n)

{

int f=1,i;

for(i=n;i>0;i--)

f=f*i;

return f;

}

For Turbo C users.

//AIM: TO FIND THE VALUE USING NEWTON FORWARD //INTERPOLATION FORMULA

#include<stdio.h>

#include<conio.h>

#define differ(b,a) (b-a)

#define m 5

int fact(int );

void main()

{

float a[m],fx[m][m],t,u,f;

float fxx=0.0,fxx1=1.0,fxx2=0.0;

int i,j;

clrscr();

printf("NEWTON FORWARD INTERPOLATION FORMULA\n");

printf("enter %d values of x\n",m);

for(i=0;i<m;i++)

scanf("%f",&a[i]);

printf("enter %d values of fx\n",m);

for(i=0;i<m;i++)

scanf("%f",&fx[i][0]);

printf("enter the value across which you want to find value\n");

scanf("%f",&t);

for(i=0;i<m;i++)

{

for(j=i;j<m;j++)

{

fx[j+1][i+1] = differ(fx[j+1][i],fx[j][i]);

}

}

printf("TABLE IS\n");

printf("x :\n");

for(i=0;i<m;i++)

printf("%f\t",a[i]);

printf("fx\t\t$fx\t\t$2fx\t\t$3fx\t\t$4fx\n");

for(i=0;i<m;i++)

{

for(j=0;j<m;j++)

{

if(j<=i)

printf("%f\t",fx[i][j]);

else

printf("\t\t");

}

}

u = ((t-a[0])/(a[1]-a[0]));

for(i=0;i<m-1;i++)

{

fxx1=fxx1*(u-i);

fxx2 = fxx2+((fxx1*fx[i+1][i+1])/(fact(i+1)));

}

fxx = fxx2+fx[0][0];

printf("the value of f(t) is: %f\n",fxx);

getch();

}

int fact(int n)

{

int f=1,i;

for(i=n;i>0;i--)

f=f*i;

return f;

}