C Program for Horner's Method

#include<stdio.h>

#include<conio.h>

#include<math.h>

float p[6], ply[6], q[6];

float synth(int m, float r){

                int i;

                q[0] = p[0];

                for(i=1;i<=m;i++){

                                q[i] = (q[i-1]*r)+p[i];

                }

                return(q[m]);

}

void main(){

                clrscr();

                int m,i,flag=0;

                float r, x,x1, b0, c1;

                printf("\t\tHORNER'S METHOD");

                printf("\n Enter the highest degree of the equation (max 5): ");

                scanf("%d",&m);

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

                                printf("\n Coefficient x[%d] = ",m-i);

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

                                ply[i] = p[i];

                                }

                printf("\n Enter the initial value x0 : ");

                scanf("%f",&r);

                x = r;

                do{

                   printf("\n%f\n",x);

                   b0 = synth(m,x);

                                for(i=0;i<=5;i++){

                                                p[i]=q[i];

                                }

                   c1 = synth(m-1,x);

                   printf("\n");

                   printf("\tb0 = %f\tc1= %f",b0,c1);

                   x1 = x - (b0/c1);

                   if(fabs(x1-x) <= 0.0009){

                                flag = 1;

                   }

                   x = x1;

                                for(i=0;i<=5;i++){

                                                p[i]=ply[i];

                                }

                   getch();

                }while(flag!=1);

                printf("\nApproximate root = %f", x1);

getch();

}

Sample Output:

                          HORNER’S METHOD
Enter the highest degree of the equation (max 5): 3
Coefficient X[3] : 1
Coefficient X[2] : 9
Coefficient X[1] : 0
Coefficient X[0] : -18
Enter the initial value X0 : 1.5
1.500000
              b0 = 5.625000   c1= 33.750000
1.333333
              b0 = 0.370371   c1= 29.333332
1.328787
              b0 =  0.002071   c1= 29.005529
Approximate root = 1.320636

©Dixit Bhatta 2013