Square Root using Newton Iteration

StormcasteR's Avatar
Newbie Member
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?
0
xpi0t0s's Avatar, Join Date: Aug 2004
Mentor
Does it work? Have you entered some test values, and did the correct results come out? If not, what results did you get?
0
StormcasteR's Avatar
Newbie Member
Quote:
Originally Posted by xpi0t0s View Post
Does it work? Have you entered some test values, and did the correct results come out? If not, what results did you get?
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...
0
asadullah.ansari's Avatar, Join Date: Jan 2008
TechCake
Check the algorithm for newton's ramson formula .. Actually wahtever you wrote the program that is by Iterative evaluation of a square root
check here also...
http://www.macs.hw.ac.uk/~pjbk/pathw...1/node124.html