//bisection method
#include<iostream>
#include<cmath>
#include<iomanip>
using namespace std;
double f(double x); //declare the function for the given equation
double f(double x) //define the function here, ie give the equation
{
double a=pow(x,3)-x-11.0; //write the equation whose roots are to be determined
return a;
}
int main()
{
cout.precision(4); //set the precision
cout.setf(ios::fixed);
double a,b,c,e,fa,fb,fc; //declare some needed variables
a:cout<<"Enter the initial guesses:\na="; //Enter the value of a(set a label('a:') for later use with goto)
cin>>a;
cout<<"\nb="; //Enter the value of b
cin>>b;
cout<<"\nEnter the degree of accuracy desired"<<endl; //Enter the accuracy
cin>>e; //e stands for accuracy
if (f(a)*f(b)>0) //Check if a root exists between a and b
{ //If f(a)*f(b)>0 then the root does not exist between a and b
cout<<"Please enter a different intial guess"<<endl;
goto a; //go back to 'a' ie 17 and ask for different values of a and b
}
else //else a root exists between a and b
{
while (fabs(a-b)>=e) /*if the mod of a-b is greater than the accuracy desired keep bisecting the interval*/
{
c=(a+b)/2.0; //bisect the interval and find the value of c
fa=f(a);
fb=f(b);
fc=f(c);
cout<<"a="<<a<<" "<<"b="<<b<<" "<<"c="<<c<<" fc="<<fc<<endl;/*print the values of a,b,c and fc after each iteration*/
if (fc==0) //if f(c)=0, that means we have found the root of the equation
{
cout<<"The root of the equation is "<<c; /*print the root of the equation and break out of the loop*/
break;
}
if (fa*fc>0) //if f(a)xf(c)>0, that means no root exist between a and c
{
a=c; /*hence make a=c, ie make c the starting point of the interval and b the end point*/
}
else if (fa*fc<0)
{
b=c; /*this means that a root exist between a and c therfore make c the end point of the interval*/
}
}
} //The loop ends when the difference between a and b becomes less than the desired accuracy ie now the value stored in 'c' can be called the approximate root of the equation
cout<<"The root of the equation is "<<c; //print the root
return 0;
}
//output attached as jpg

PhD researcher at Friedrich-Schiller University Jena, Germany. I'm a physicist specializing in theoretical, computational and experimental condensed matter physics. I like to develop Physics related apps and softwares from time to time. Can code in most of the popular languages. Like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

It’s also known as error tolerance.
It implies, that the roots determined at two successive iterations don’t differ more than the degree of accuracy.
This means that the calculations have converged to the tolerance desired. So, for example if you set a tolerance of 0.0001, then the program stops iterating when the root at the current iteration doesn’t differ from the root at the previous iteration by more than 0.0001.
So, this means that the root has converged upto 3 decimal places. So, the numerical root would match the numerical root till 3 decimal places.
A much tighter convergence criteria, implies a very small value of error tolerance, ex: 0.0000001. But this may take a lot of iterations.
Here, is another much rigorous definition: https://en.wikipedia.org/wiki/Order_of_accuracy

Your loop Has to be do_while.

tnx i like the code but i want to know what did you mean when you say degree of accuracy desired

do you have the flow chart in detail for bisection and newton’s raphson method? Please

sir,what does you mean by degree of accuracy?

Are you talking about iteration or something else?

It’s also known as error tolerance.

It implies, that the roots determined at two successive iterations don’t differ more than the degree of accuracy.

This means that the calculations have converged to the tolerance desired. So, for example if you set a tolerance of 0.0001, then the program stops iterating when the root at the current iteration doesn’t differ from the root at the previous iteration by more than 0.0001.

So, this means that the root has converged upto 3 decimal places. So, the numerical root would match the numerical root till 3 decimal places.

A much tighter convergence criteria, implies a very small value of error tolerance, ex: 0.0000001. But this may take a lot of iterations.

Here, is another much rigorous definition: https://en.wikipedia.org/wiki/Order_of_accuracy