CPNM LAB PROGRAM-9

 

9. Implement bisection method to find the square root of a given number to a given accuracy.

Algorithm: 

Step – 1 : Start 

Step – 2 : Read a, b, epsilon, xmid 

Step – 3 : Enter the no. for which square root has to be found 

Step – 4 : Enter the initial guess values and accuracy 

Step – 5 : If(f(a) * f(b) > 0) 

Step – 6 : Print unsuitable initial values 

Step – 7 : Exit 

 Step – 8 : Xmid = (a + b) / 2 

Step – 9 : While(fabs(xmid - b) / xmid >= epsilon) 

Step – 10 : If f(xmid == 0) 

Step – 11 : Break 

Step – 12 : If(f(a) * f(xmid) < 0) 

Step – 13 : B = xmid 

Step – 14 : Else a = xmid 

Step – 15 : Xmid = a + b / 2 

Step – 16 : Go to Step–10 

 Step – 17 : Print the square root is xmid 

Step – 18 : Stop

Program:-

#include<stdio.h>

#include<conio.h>

#include<stdlib.h>

#include<math.h>

 float n; 

 float f(float x)

{ return(x * x - n);  }

     main() 

{

float a, b, epsilon, xmid; 

clrscr(); 

printf("\nEnter the no. of which square root has to be found :\n"); 

scanf("%f",&n);

printf("\nEnter the initial guess values and accuracy: \n"); 

scanf("%f,%f,%f",&a, &b, &epsilon); 

if(f(a) * f(b) > 0)

{

printf("\n Unsuitable initial values \n"); exit(0);

}

xmid = (a + b) / 2;

while(fabs(xmid - b) / xmid >= epsilon)

{

if(f(xmid) == 0) 

{  break;  }

if(f(a) * f(xmid) < 0) 

{b = xmid;}

 else 

{a = xmid;

 xmid = (a + b) / 2;}

}

printf("\nThe Square root = %2f \n",xmid); 

getch(); return 0;

} 

  

THIS CODE IS CREATED BY ECE THE WONDERS, HEMU THE SMART

output :-

Run 1:

 

Enter the no. of which square root has to be found :

25

 

Enter the initial guess values and accuracy:

4,6,0.0001

 

The Square root = 5.000000

 

Run 2:

 

Enter the no. of which square root has to be found :

49

 

Enter the initial guess values and accuracy:

4,6,0.0001

 

Unsuitable initial values