Implement Newton’s backward interpolation polynomial using C programming.

#include

#include

void main()

{

            clrscr();

            int i,j,n,k;

            float f[30],x[30],df[30][30],xx,a,b,mul,ad,x0,f0;

            printf ("\t\tNewton's Backward Interpolation\n");

            printf ("\t\t------------------------------\n\n");

            printf("How many points???");

            scanf("%d",&n);

            for(i=0;i

            {

                        printf("\nEnter the value of x[%d]:",i);

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

                        printf("Enter the value of f[x%d]:",i);

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

                        df[0][i]=f[i];

            }

            printf("\n Enter the value x:");

            scanf("%f",&xx);

            a=x[1]-x[0];

            for(i=0;i

            {

                        df[i][1]=f[i+1]-f[i];

            }

            for(j=2;j

            {

                        for(i=0;i

                        {

                                    df[i][j]=df[i+1][j-1]-df[i][j-1];

                        }

            }

            i=0;

            while (!x[i]>xx)

            {

            i++;

            }

            x0=x[0];

            f0=f[0];

            b=(xx-x0)/a;

            mul=1;

            ad=f0;

            for(k=1;k<=n;k++)

            {

                        mul=(mul*(b-(k-1)))/k;

                        ad=ad+(mul*df[i][k]);

            }

            printf("\n The required value = %4f",ad);

            getch();

}