二分法和牛顿迭代法解方程c++实现代码

二分法和牛顿迭代法都是求解方程的方法，下面分别给出 C++ 实现代码：

1. 二分法：

#include <iostream>
using namespace std;

double func(double x) {  //定义方程
    return x * x - 2;
}

double bisection(double a, double b, double eps) {  //二分法求解方程
    double mid = (a + b) / 2;
    while (b - a > eps) {
        if (func(mid) == 0) return mid;
        else if (func(a) * func(mid) < 0) b = mid;
        else a = mid;
        mid = (a + b) / 2;
    }
    return mid;
}

int main() {
    double result = bisection(1, 2, 0.00001);
    cout << "The root of the equation is: " << result << endl;
    return 0;
}

2. 牛顿迭代法：

#include <iostream>
using namespace std;

double func(double x) {  //定义方程
    return x * x - 2;
}

double func_derivative(double x) {  //定义方程的导数
    return 2 * x;
}

double newton(double x0, double eps) {  //牛顿迭代法求解方程
    double x1 = x0 - func(x0) / func_derivative(x0);
    while (abs(x1 - x0) > eps) {
        x0 = x1;
        x1 = x0 - func(x0) / func_derivative(x0);
    }
    return x1;
}

int main() {
    double result = newton(1, 0.00001);
    cout << "The root of the equation is: " << result << endl;
    return 0;
}