用牛顿法求方程的根x^2-e^x＝0的C++程序代码

使用牛顿迭代法求解非线性方程 `f(x) = x^2 - e^x = 0` 的C++程序代码可以如下所示：

#include <iostream>
#include <cmath>

double function(double x) {
    return pow(x, 2) - exp(x);
}

double derivative(double x) {
    return 2 * x - exp(x);
}

double newtonRaphson(double x0, double epsilon, int maxIterations) {
    if (epsilon <= 0) {
        std::cerr << "Error: Epsilon must be a positive value." << std::endl;
        return 0;
    }
    
    int iteration = 0;
    double nextX = x0;

    while (iteration < maxIterations && abs(function(nextX)) > epsilon) {
        nextX -= function(nextX) / derivative(nextX);
        iteration++;
    }

    if (iteration == maxIterations) {
        std::cout << "Warning: Maximum number of iterations reached (" << maxIterations << "). No solution found within the specified tolerance." << std::endl;
    }

    return nextX;
}

int main() {
    const double initialGuess = 0; // 初始猜测值
    const double tolerance = 1e-6; // 求解精度
    const int maxIter = 100; // 最大迭代次数

    double root = newtonRaphson(initialGuess, tolerance, maxIter);
    if (root != 0) {
        std::cout << "The root of the equation is approximately: " << root << std::endl;
    }

    return 0;
}

这个程序首先定义了函数 `function` 和其导数 `derivative`，然后实现了牛顿法 `newtonRaphson`，该方法接受初始猜测值、容差和最大迭代次数作为输入。如果找到满足条件的根，则返回结果；否则给出警告信息。