C++求解牛顿迭代法的Polynomial.h 头文件

下面是一个简单的Polynomial类的头文件，其中包含了牛顿迭代法的实现：

#include <vector>

class Polynomial {
public:
    Polynomial(std::vector<double> coeffs);
    double operator()(double x) const;
    Polynomial derivative() const;
    double newton(double x0, double eps, int max_iters) const;

private:
    std::vector<double> coeffs_;
};

Polynomial::Polynomial(std::vector<double> coeffs) : coeffs_(std::move(coeffs)) {}

double Polynomial::operator()(double x) const {
    double result = 0;
    for (int i = coeffs_.size() - 1; i >= 0; --i) {
        result = result * x + coeffs_[i];
    }
    return result;
}

Polynomial Polynomial::derivative() const {
    std::vector<double> der_coeffs;
    for (int i = 1; i < coeffs_.size(); ++i) {
        der_coeffs.push_back(i * coeffs_[i]);
    }
    return Polynomial(der_coeffs);
}

double Polynomial::newton(double x0, double eps, int max_iters) const {
    double x = x0;
    for (int i = 0; i < max_iters; ++i) {
        double fx = (*this)(x);
        double fx_deriv = derivative()(x);
        if (std::abs(fx_deriv) < eps) {
            throw std::runtime_error("Newton iteration failed: zero derivative");
        }
        double x_new = x - fx / fx_deriv;
        if (std::abs(x_new - x) < eps) {
            return x_new;
        }
        x = x_new;
    }
    throw std::runtime_error("Newton iteration failed: maximum iterations exceeded");
}

在这个头文件中，`Polynomial`类表示一个多项式，使用一个`std::vector<double>`来存储多项式系数。`operator()`方法用于计算多项式在给定点的值，`derivative()`方法用于计算多项式的导函数，`newton()`方法用于使用牛顿迭代法求解多项式的根。注意，在`newton()`方法中，我们使用`derivative()`方法来计算导函数。