Regula Falsi Method

     Algorithm : Regula-Falsi Method

Regula_falsi(a,b)
	{
Let us consider a function f(x)=0. This algorithm finds a root of f(x)=0 between a and b.

	error = 10-6
      if(f(a)*f(b)>0)		//f(a) is a function
	{			which returns the value of f(x) at  x=a
	    print “Root not lie between [a,b]”  
        }						  
	else
		{
		c=a+((|f(a)|/(f(a)+f(b)))*(b-a))
     do
	{
	    fc=f(c)
	    fa=f(a)
	    fb=f(b)
	     if(fc=0)
		{
		print “The root is c”
		return
                }
	      else
	        {
		  if(fc<0)
		   {
			if(fa<0)
			a=c
			else
	                b=c
                   }
		else if(fc>0)
		{
		  if(fa>0)
		   a=c
                   else
	           b=c
                 }
	cprev=c
       c= a+((|f(a)|/(f(a)+f(b)))*(b-a))
   }
}
   while(|cprev-c|>error)
   print “The root is c”
  }
}

C Program For Regula Falsi Method

Source Code:

#include<stdio.h>
#include<conio.h>
#include<math.h>

void regula(float,float);
float f(float);
void main()
{
 int i;
 clrscr();
 printf("\nThe equation is : x^3-9x+1=0\n");
 for(i=-32768;i<32767;i++)
 {
  if(f(i)*f(i+1)<0)
 regula(i,i+1);
 }
 getch();
}

void regula(float a,float b)
{
 float error,c,Cprev,FA,FB,FC;
 error=0.000001;
 printf("a         f(a)         b         f(b)        c        f(c)      ");
 printf("\n----------------------------------------------------------------------");
  FA=f(a);
   FB=f(b);
  c=a+(fabs(f(a))/(fabs(f(a))+fabs(f(b))))*fabs(b-a);
  do
  {
   FA=f(a);
   FB=f(b);
   FC=f(c);
printf("\n%f   %f   %f   %f   %f   %f   ",a,FA,b,FB,c,FC);
   if(FC==0)
   {
    printf("\n\nThe root is %f\n\n",c);
    return;
   }
   else
   {
    if(FC<0)
    {
     if(FA<0)
      a=c;
     else
      b=c;
    }
    else
    {
     if(FA>0)
      a=c;
     else
      b=c;
    }
   }
    Cprev=c;
    c=a+(fabs(f(a))/(fabs(f(a))+fabs(f(b))))*fabs(b-a);
   }while(fabs(Cprev-c)>error);
   printf("\nThe root is %f\n",c);
  }

float f(float x)
{
 return (x*x*x-9*x+1);
}



OUTPUT :

The equation is : x^3-9x+1=0

a         f(a)         b         f(b)        c        f(c)
----------------------------------------------------------------------
-4.000000   -27.000000   -3.000000   1.000000   -3.035714   0.345616
-4.000000   -27.000000   -3.035714   0.345616   -3.047902   0.117005
-4.000000   -27.000000   -3.047902   0.117005   -3.052010   0.039333
-4.000000   -27.000000   -3.052010   0.039333   -3.053389   0.013191
-4.000000   -27.000000   -3.053389   0.013191   -3.053851   0.004420
-4.000000   -27.000000   -3.053851   0.004420   -3.054006   0.001483
-4.000000   -27.000000   -3.054006   0.001483   -3.054058   0.000496
-4.000000   -27.000000   -3.054058   0.000496   -3.054075   0.000166
-4.000000   -27.000000   -3.054075   0.000166   -3.054081   0.000057
-4.000000   -27.000000   -3.054081   0.000057   -3.054083   0.000021

The root is -3.054084

a         f(a)         b         f(b)        c        f(c)
----------------------------------------------------------------------
0.000000   1.000000   1.000000   -7.000000   0.125000   -0.123047
0.000000   1.000000   0.125000   -0.123047   0.111304   -0.000360
0.000000   1.000000   0.111304   -0.000360   0.111264   -0.000001

The root is 0.111264

a         f(a)         b         f(b)        c        f(c)
----------------------------------------------------------------------
2.000000   -9.000000   3.000000   1.000000   2.900000   -0.710998
2.900000   -0.710998   3.000000   1.000000   2.941555   -0.021475
2.941555   -0.021475   3.000000   1.000000   2.942783   -0.000623
2.942783   -0.000623   3.000000   1.000000   2.942819   -0.000020
2.942819   -0.000020   3.000000   1.000000   2.942820   0.000000

The root is 2.942820