Secant Method Implementation in C

secant.c

/* This method is quite similar to that of the Regula-Falsi method except for the
condition f(x1).f(x2) < 0. Here the graph of the function y = f(x) in the
neighborhood of the root is approximated by a secant line or chords. Further,
the interval at each iteration may not contain the root.
Let the limits of interval initially be x0 and x1.

Then the first approximation is given by:
         x2 = x1 – [(x1-x0)/f(x1)-f(x0)]f(x1)
Again, the formula for successive approximation in general form is
         x(n+1) = xn - [xn - x(n-1)/f(xn)-f(x(n-1))]f(xn) */

/********* PROGRAM STARTS HERE *********/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

/********* FUNCTION DECLARATION *********/
void secant(float a, float b);
float function(float val);
void check_bound(float a);

/********* MAIN STARTS HERE *********/
int main(int argc, char **argv)
{
   float        a, b;

   if (argc != 3)
   {
      printf("Usage: %s <root1> <root2>\n", argv[0]);
      exit(1);
   }

   a = atof(argv[1]);
   b = atof(argv[2]);

   printf("By using Secant method: \n");
   printf("The equation is: \n");
   printf("\t");
   printf("f(x) = x^4 - 26x^2 + 49x - 25\n");

   printf("----------------------\n");
   printf("   f(a)    f(b)     \n");
   printf("----------------------\n");

   secant(a, b);  //Calling Function

   exit(0);
}

/********* FUNCTION DEFINITION *********/
void secant(float a, float b)
{
   float        fa, fb, root, i = 0;

   while (1)
   {
      fa = function(a);
      fb = function(b);

      root = (a*fb - fa*b)/(fb-fa);
      printf("%f   %f\n", fa, fb);

      a = b;
      b = root;
      if (floorf(a*10000) == floorf(b*10000))  //Checking roots
      {
         printf("The root is %f found after %.1f iterations.\n", root, i);
         break;
      }
      i++;  //Incrementing i
   }

   return ;
}

float function(float val)
{
   float        fx, x = val;  //Declaration of variables in float

   fx = (x * x * x * x) - (26 * x * x) + 49 * x - 25;  // Function
   return fx;  //Returning the value of f(x) at x1
}

void check_bound(float a)
{
   float        fa;  //Declaration of variables in float

   fa = function(a);  //Calling Functions

   if (fa == 0)  //Check condition
   {
      printf("The root is one of the boundaries.\n");
      exit(0);
   }

   return ;
}