牛頓法範例

newton_sqrt2.cpp

#include <iostream>
using namespace std;

double f(double x) {
	return x * x - 2; // f(x) = x^2 - 2 = 0, to find x^2=2, x = ?
}

double f_diff(double x, double h=1e-6) {
	return (f(x + h) - f(x)) / h;
}

double newton(double x_init, int N) {
	double x = x_init;
	for (int i = 0; i < N; i++) {
		double x_next = x - (f(x) / f_diff(x));
		x = x_next;
	}
	return x;
}

int main() {
	double x;
	int N;
	cout << "Please enter a initial point: ";
	cin >> x;
	cout << "Please enter the times to apply the Newton method: ";
	cin >> N;
	cout << "We have the root: " << newton(x, N) << endl;
	return 0;
}
double f_diff(double x, double h=1e-6) {
  return (f(x+h)-f(x)) / h;
}