Bisection Method

This method is also called "Mid-Point Method".
ALGORITHM:

1. START.
2. Input initial values x1 and x2.
3. Compute f1=f(x1) and f2=f(x2).
4. If f1*f2>0, x1 and x2 do not bracket the the root and go to step 2.
5. Compute xm=(x1+x2)/2 and fm=f(xm).
6. If f1*fm<0, set x2=xm and set f2=fm, Else x1=xm and f1=fm.
7. If |(x2-x1)/xm|<accuracy, then root = xm, Else go to step 5.
8. STOP

PROGRAM in C:

#include<stdio.h>

#include<math.h>

#include<conio.h>

float f(float x)

{

  return(x*x*x+x*x-3*x-3);

}

void main()

{

  float x1,x2,xm=0,tmp,eps=0.0001;

  int iteration=0;

  do

  {

    printf("Enter Initial guess");

    scanf("%f %f", &x1,&x2);

    if(f(x1)*f(x2)>0)

      printf("\nInvalid Guess.... Type the guess again...\n");

  }while(f(x1)*f(x2)>0);

  do

  {

    tmp=xm;

    xm=(x1+x2)/2.00;

    iteration++;

    if(f(x1)*f(xm)<0)

        x2=xm;

    else

        x1=xm;

  }while(fabs(xm-tmp)>eps);

  printf("\n Result = %.5f   Iteration=%d",xm,iteration);

  getch();

}

False-Position Method >>