C++ 高斯牛顿法代码示例：求解方程根

#include #include

using namespace std;

double f(double x) { return cos(x) - x; }

double df(double x) { return -sin(x) - 1; }

double d2f(double x) { return -cos(x); }

double newton(double x0) { double x = x0; double epsilon = 0.00001; int max_iterations = 100;

for (int i = 0; i < max_iterations; i++) {
    double f_x = f(x);
    double df_x = df(x);
    double d2f_x = d2f(x);

    if (abs(f_x) < epsilon) {
        cout << "Converged after " << i << " iterations." << endl;
        return x;
    }

    x = x - f_x / df_x;

    if (abs(f_x / df_x) < epsilon) {
        cout << "Converged after " << i << " iterations." << endl;
        return x;
    }

    if (abs(d2f_x / df_x) > epsilon) {
        cout << "Diverged after " << i << " iterations." << endl;
        return NAN; // Not a number
    }
}

cout << "Reached maximum number of iterations without converging." << endl;
return NAN;

}

int main() { double x0 = 1.0; // Initial guess double root = newton(x0); cout << "Root: " << root << endl; return 0; }