False-Position Method

This method is also called "Regula Falsi 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 x=x1-(f(x1)*(x2-x1))/((f(x2)-f(x1)) and fx=f(x).
6. If f1*fx<0, set x2=x and set f2=fx, Else x1=x and f1=fx.
7. If |(x2-x1)/x|<accuracy, then root = x, Else go to step 5.
8. STOP

PROGRAM in C:

#include<stdio.h>

#include<conio.h>

#include<math.h>

float f(float x)

{

  return(x*x*x-2*x-5);

}

void main()

{

  float x1,x2,x=0,tmp,eps=0.001;

  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

  {

    iteration++;

    tmp=x;

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

    if(f(x1)*f(x)<0)

        x2=x;

    else

        x1=x;

  }while(fabs(tmp-x)>eps);

  printf("\n Result = %.4f Iteration=%d",x,iteration);

  getch();

}

Newton-Raphson Method >>