C++ Newton iterative method to solve nonlinear equations

Newton iteration method algorithm:

Thought:

Divide the nonlinear equation into linear equations infinitely, and iterate using the triangular relationship of the slope (derivative) of the linear equation:

1. Given an initial solution x0
2. Calculate f(x0) and df(x0)
3. Update x0=x0 - ((f(x0)) / (df(x1)));
4. End if the change is less than the threshold or the number of iterations is reached
5. Repeat the above process.

C++ tearing Newton iteration method

Example:
Use Newton's method to solve a real root of the equation f(x)=(x*e^x)-1=0 in [0,1], take the initial point x0=0.5 and the precision is e-5

//牛顿迭代解非线性方程组
#include <iostream>
#include <cmath>
using namespace std;

//非线性方程
double f(double x) {
    
    
	double f = x * exp(x) - 1;
	return f;
}
//求导
double df(double x) {
    
    
	double df = (x + 1) * exp(x);
	return df;
}

double EPS;
//迭代
double Newton(double x0)
{
    
    

	double x1 = 0;
	int itCount = 0;//迭代次数
	do
	{
    
    
		if (itCount)
			x0 = x1;

		x1 = x0 - ((f(x0)) / (df(x1)));
		cout << " 第" << ++itCount <<"次迭代后x="<<x1<< endl;
	} while (abs(x1 - x0) > EPS);

	return x1;

}

void main()
{
    
    

	double x;

	cout << " 请输入初值 x0: ";
	cin >> x;
	cout << "请输入EPS:";
	cin >> EPS;
	x = Newton(x);
	cout << " 达到计算精度使f(x)=0的解为: " << x << endl;
	cout << endl;
	system("pause");
}