Tag: newton-raphson-method

#include <math.h>
#include <iostream>
using namespace std;

long double f(long double x)
{
	return powl(8.0, x) - powl(2.0, x) -
		2.0 * (powl(6.0, x) - powl(3.0, x));
}

long double g(long double x)
{
	return powl(8.0, x) * logl(8.0) - powl(2.0, x) * logl(2.0) -
		2.0 * (powl(6.0, x) * logl(6.0) - powl(3.0, x) * logl(3.0));
}

long double Newton(long double x, int maxIts, int& iterations)
{
	long double x0 = x;
	long double x1 = 0.0;
	
	iterations = 0;

	while (true) {
		long double dx = 0.0;
		long double fx = f(x0);
		long double gx = g(x0);
		x1 = x0 - fx / gx;
		dx = fabsl(x1 - x0);
		iterations++;
		if (dx < 1.0e-15)
			break;
		if (fabsl(fx) < 1.0e-15)
			break;
		if (iterations == maxIts)
			break;
		x0 = x1;
	}

	return x1;
}

int main() {
	int iterations = 0, maxIts;
	long double x0 = 0.0, x1 = 0.0;

	while (true) {
		cout << "x0 = ";
		cin >> x0;
		if (x0 == 0)
			break;
		cout << "maximum iterations = ";
		cin >> maxIts;
		x1 = Newton(x0, maxIts, iterations);
		cout << "x1 = " << x1 << endl;
		cout << "iterations = ";
		cout << iterations << endl;
	}

	return 0;
}