Newbie Newton Algorithm and extra precision digits

*To*: mathgroup at smc.vnet.net*Subject*: [mg47875] Newbie Newton Algorithm and extra precision digits*From*: Benjamin Collas <adresse.secours at libertysurf.fr>*Date*: Thu, 29 Apr 2004 03:05:59 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Here is another mystery (I think there's something I dont understand with N). I'm using the Newton algorithm to compute one root of X^2-2 : with NestWhile I can iterate the fixed point formula. My stop test is (Abs[#2-#1]>10^(-6))&, and the Mathematica answer is 1.41421. The problem is when I ask Precision[%], Mathematica returns MachinePrecision (ie 15.9546 by default)... More over, when I copy-past the 1.41421 answer, what displays is 1.414235623730951' which means that Mathematica knows this number with 16 digits... But how could it be as my stop test is about 10^(-6). As Newton is a quadratic computional method, the best I could have is a 6 or 12 precision digits. Can anyone explains where am I wrong ? Regards, Benjamin Collas PS : thank you Jens-Peer Kuska for your help,I'm so confused not to have find it out by myself...