Secant Method

This method is also called "Chord Method".

ALGORITHM:

1. START.
2. Input initial values x1 and x2.
3. Compute x_i+1 = x_i - (f(x_i)(x_i-x_i-1))/(f(x_i)(x_i-x_i-1)) for i=2,3,4,.....
4. Next, x_i-1 is replaced by x_i and x_i by x_i+1 in the iteration process.
5. If |(x_i - x_i-1)/ x_i+1| < accuracy, then root = x_i+1 , Else go to step 3.
6. STOP.

PROGRAM in C:

#include<stdio.h>

#include<math.h>

#include<conio.h>

float f(float x)

{

  return(x*exp(x)-cos(x)); /* xex = cos x */

}

void main()

{

  float x1,x2,x=0,eps=0.0001,tmp;

  int iteration=0;

  printf("\nEnter two guesses:");

  scanf("%f %f",&x1,&x2);

  do

  {

    tmp=x;

    x=(f(x2)*x1-f(x1)*x2)/(f(x2)-f(x1));

    iteration++;

    x1=x2;

    x2=x;

  }while(fabs(tmp-x)>eps);

  printf("\nRoot=%.5f \t Iteration=%d",x,iteration);

  getch();

}

Fixed-Point Iteration Method >>