C++中的牛顿法

Question

您好，我已经检查了许多其他问题，但似乎无法弄清楚为什么我的实现不会收敛。即使进入根目录，我也一直在获取程序的 "Error, no convergence" 部分。

函数是 y = x^2 - 1

代码如下：

// Newton sqaure root finder function

#include <iostream>
#include <cmath>

int main()
{
using namespace std;

// Enter an initial guess x
cout << "Enter an initial guess: ";
double x;
cin >> x;


// Define & initialize the error, tolerance and iteration variables
double tol = 1e-12;
cout << 1e-12;
double error = tol + 1; 
int it = 0;
int max_it = 100;

// Define the x1 variable to hold the latest result (root approximation)
double x1;

// Start while loop with guess x to find the root
while (error > tol && it < max_it)
{
    x1 = x + (x*x-1) / (2*x);
    error = fabs(x1 - x);
    x = x1;
    it++;
    cout << error << endl;
}

if (error <= tol)
{
    cout << "The root is " << x << endl;
} 
else
{
    cout << "Error, no convergence" << endl;
}

cin.get();
cin.get(); 

return 0;
}

Answer 1

你的公式有误

x1 = x + (x*x-1) / (2*x);

应该是

x1 = x - (x*x-1) / (2*x);

您可能会在这里看到：https://en.wikipedia.org/wiki/Methods_of_computing_square_roots

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