Secant Method

 Algorithm : Secant Method

Secant(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
	{
	p0=a
	p1=b
	p2=pi-f(p1)*(p1-p0)/(f(p1)-f(p0))
	do
		{	 
		   p0=p1 					
		   p1=p2			   
                   p2=pi-f(p1)*(p1-p0)/(f(p1)-f(p0))
                }
    while(|p1-p2|<error)		   
    print “p2”
  }
}


C Program For Secant Method

Source Code:

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

void secant(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)
 secant(i,i+1);
 }
 getch();
}

void secant(float m,float n)
{
 float error,c,a,b;
 error=0.000001;
 a=m;
 b=n;
 c=b-((f(b)*(b-a))/(f(b)-f(a)));
 printf("a         f(a)         b        f(b)       c     ");
 printf("\n-----------------------------------------------------------");

  do
  {
   a=b;
   b=c;
   c=b-((f(b)*(b-a))/(f(b)-f(a)));
   printf("\n%f   %f   %f   %f   %f",a,f(a),b,f(b),c);
  }while(fabs(b-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
-----------------------------------------------------------
-3.000000   1.000000   -3.035714   0.345616   -3.054577
-3.035714   0.345616   -3.054577   -0.009359   -3.054080
-3.054577   -0.009359   -3.054080   0.000084   -3.054084
-3.054080   0.000084   -3.054084   -0.000002   -3.054084

The root is -3.054084

a         f(a)         b        f(b)       c
-----------------------------------------------------------
1.000000   -7.000000   0.125000   -0.123047   0.109344
0.125000   -0.123047   0.109344   0.017212   0.111265
0.109344   0.017212   0.111265   -0.000009   0.111264
0.111265   -0.000009   0.111264   0.000000   0.111264

The root is 0.111264

a         f(a)         b        f(b)       c
-----------------------------------------------------------
3.000000   1.000000   2.900000   -0.710998   2.941555
2.900000   -0.710998   2.941555   -0.021475   2.942849
2.941555   -0.021475   2.942849   0.000486   2.942820
2.942849   0.000486   2.942820   0.000000   2.942820

The root is 2.942820