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Square Root using Newton Iteration

Discussion in 'C++' started by StormcasteR, Jan 16, 2009.

  1. StormcasteR

    StormcasteR New Member

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    So.Dudes heres the deal.Yesterday a friend of mine wanted me to help him with a function that calculates square root of a positive number using Newton's method.So I came up with this:
    Code:
    #include <iostream>
    #include <cmath>
    using namespace std;
    int main()
    {
      const double tol = 0.000005;
      double value;
      double old_app, new_app;
      cout << "Square root of a number"
           << endl << endl;
      cout << "Enter a positive number: ";
      cin >> value;
      if (value < 0.0)
        cout << "Cannot find square root of negative number"
             << endl;
      else
         if (value == 0.0)
            cout << "square root of "
                 << value
                 << " is 0.00"
                 << endl;
         else
           {
             old_app = value;
             new_app = (old_app + value/old_app)/2;
             while (fabs((new_app-old_app)/new_app) > tol)
               {
                 old_app = new_app;
                 new_app = (old_app + value/old_app)/2;
               }
             cout << "square root of "
                  << value
                  << " is " << new_app
                  << endl;
                  system ("pause");
           }
    }
    
    But I'm really new in C++ and I'm not sure if this is the right way to represent this algorithm?
     
  2. xpi0t0s

    xpi0t0s Mentor

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    Does it work? Have you entered some test values, and did the correct results come out? If not, what results did you get?
     
  3. StormcasteR

    StormcasteR New Member

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    Yes.I entered 78.32for example and the program outputs 8.84986 for square root.Another program I wrote uses heron's formula and the output is the same ( 8.84986) while the normal cmath sqrt() function outputs 8.83176.Anyway, the program works properly but I'm not sure if this is the right way for Newton's method and if the formula I'm using is correct...
     
  4. asadullah.ansari

    asadullah.ansari TechCake

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