Iteration_Method.c

//C Program to Implement Iteration Method
#include<stdio.h>
#include<math.h>
#define EPSILON 0.001

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

float findValueAt(float x)
{
    return 1/sqrt(1+x);
}
float differentiate(float x)
{
    return 1/2.0 * (pow(1,pow((1+x),3/2.0)));
}

int main()
{
    int maxIteration,i;
    float a,b,x,x0;
    printf("Enter Maximum no of Iterations\n");
    scanf("%d",&maxIteration);

//......Compute a and b............. 
   
   do
   {
        printf("Enter the value of a and b(starting boundary)");
        scanf("%f%f",&a,&b);
        if(f(a)*f(b)>0)
        {
           printf("Boundary Values are Invalid\n");
           continue;
        }
        else
        {
            printf("Roots Lie between %f and %f\n",a,b);
            break;
        }
    } while(1);

    //find x0
    x0= (a+b)/2;
    //check if the function form used is valid or invalid
    if(fabs(differentiate(x0))<1)
        printf("Function Form is Correct. Iteration Method can be applied\n");
    else
    {
        printf("Function Form is NOT Correct. Iteration Method CAN'T be applied\n");
        return 0;
    }

    //Apply Successive approximation to find the root b/w a and b
    //..........Find root............   
    
    for(i=1;i<=maxIteration;i++)
    {
      x = findValueAt(x0);   //find the mid point
      
      if(fabs(x-x0)<EPSILON)
      {
           printf("Iterations=%d  Final Root=%f\n",i,x);
           return 0;
      }      
      printf("Iterations=%d  Roots=%f\n",i,x); 
      x0=x;
    }
    printf("Root=%f  Total Iterations=%d",x,--i);
    return 0;
}