The Newton Raphson Method is an open method used to find the roots of a function.
It employs the technique of linear approximation and involves using the tangent line to approximate the roots.
The method is highly efficient and converges rapidly, providing robust solutions in fewer iterations.
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{{{{{
#include <iostream>
#include <cmath>
using namespace std;
const double EPS = 0.000001;
double function(double x0)
{
// x0^2 - 3*x0 + 2 = (x0 - 1)(x0 - 2)
return x0*x0 - 3*x0 + 2;
}
double derivative_of_the_function(double x0)
{
return 2*x0 - 3;
}
int main()
{
int max;
int i = 0;
double x1, x0;
cout << "Newton-Raphson Method in C++" << endl;
cout << "Maximum number of iterations: ";
max = 100;
cout << max << endl;
cout << "The first approximation: ";
x0 = 0; // you get the root 1
//x0 = 3; // you get the root 2
cout << x0 << endl;
bool flagStopLoop = false;
do
{
x1 = x0 - (function(x0) / derivative_of_the_function(x0));
i++;
if( fabs(x1 - x0) <= EPS )
{
flagStopLoop = true;
}
else if( i > max )
{
flagStopLoop = true;
}
else
{
x0 = x1;
}
} while( !flagStopLoop );
cout << "The root of the function after " << i << " iteration is "
<< x1 << endl;
return 0;
}
}}}}}
