Newton-Raphson Method

newton.cpp

/*
 *  ------------------------
 *  | Newton-Raphson Method |
 *  ------------------------
 *
 *  Author: Navin Mohan
 *  Website: https://nvnmo.github.io
 *
 *  MIT License
 *
 *  Copyright (c) 2019 Navin Mohan
 *  
 *  Permission is hereby granted, free of charge, to any person obtaining a copy
 *  of this software and associated documentation files (the "Software"), to deal
 *  in the Software without restriction, including without limitation the rights
 *  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 *  copies of the Software, and to permit persons to whom the Software is
 *  furnished to do so, subject to the following conditions:
 *  
 *  The above copyright notice and this permission notice shall be included in all
 *  copies or substantial portions of the Software.
 *  
 *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 *  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 *  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 *  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 *  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 *  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 *  SOFTWARE.
 *
*/
#include <iostream>
#include <cmath>

using namespace std;

double f(double x){
    // the function
    return log(x) - cos(x);
}

double f_prime(double x){
    // the derivate 
    return 1/x + sin(x);
}

double approximate(double (*f) (double), double (*f_prime) (double),double x,int n){
    while(n--){
        // f_prime(x) is assumed to be non-zero
        x = x - f(x)/f_prime(x);
    }

    return x;
}

int main(){
    double x;
    int n;
    cout << "X0 = ";
    cin >> x;
    cout << "Number of iterations: ";
    cin >> n;
    cout << approximate(f,f_prime,x,n) << endl;
    return 0;
}