Coding the Regula Falsi

The convergce process in the bisection method is very slow. It depends only on the choice of end points of the interval [a,b]. The function f(x) does not have any role in finding the point c (which is just  the mid-point of a and b). It is used only to decide the next smaller interval [a,c] or [c,b]. A better approximation to c can be obtained by taking the straight line L joining the points (a,f(a)) and (b,f(b)) intersecting the x-axis. To obtain the value of c we can equate the two expressions of the slope m of the line L.

Let's take an Equation   :-  x*x*x-17

#include<stdio.h>

 struct iter

 {

     float x1;

     float x0;

 };

 float f(float x)

 {

    float y;

    y=x*x*x-17;

    return y;

 }

 float f1(float x)

 {

     float y1;

      y1=3*x*x;

      return y1;

 }

 void main()

 {

     int n,i;

     float a,b,x0,x1,x2,x3,x4,x5,x6;

     printf("enter the intervals");

     scanf("%f%f" ,&a,&b);

     printf("\nEnter the number of iterations\n");

     scanf("%d",&n);

     if(f(a)*f(b)<0)

     {

         printf("root is possible between interval %f %f " ,a,b);

     }

     else

     {

    printf("root does not lie between %f %f \n" ,a,b);

    exit(1);

     }

 if(fabs(f(a))<fabs(f(b)))

 x0=f(a);

 else

 x0=f(b);

 x0=a;

 printf("xnot is %f \n " ,x0 );

struct iter k[1000];

 k[0].x0=x0;

i=0;

while(n!=0)

{

  k[i].x1=k[i].x0-(f(k[i].x0)/f1(k[i].x0));

 printf("\n%f" ,k[i].x1);

 k[i+1].x0= k[i].x1;

--n;

++i;

}

 }