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Re: Default Precision isn't reached yet no warning about convergence are generated

• To: mathgroup at smc.vnet.net
• Subject: [mg44658] Re: [mg44653] Default Precision isn't reached yet no warning about convergence are generated
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 20 Nov 2003 03:16:24 -0500 (EST)
• References: <200311190959.EAA22301@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 19 Nov 2003, at 18:59, Michael Beqq wrote:

> I have some doubts about solutions found by FindRoot.  I solved some
> equation f[x]=0 and found some x*.  Now, if I plug x* back into f[x] 
> then I
> should get zero or something close to zero based on MaxPrecision, 
> which is,
> I believe, is equal to 10^-50.  However, I get f[x*]=10^-9 which is a 
> lot
> less than 10^-50 yet while solving FindRoot does not give me any 
> warnings
> about failure to coverge.  This is true for both Newton and Secant 
> method.
> I increased precision to 200, MaxPrecision->200, but the results are 
> the
> same.  Shall I accept solutions found by Mathematica as true 
> solutions?  I
> have version 4.0. Thanks.
>
>
>
You should increase WorkingPrecision, not just MaxPrecision. Also, 
check the precision of your input. It should be at least as precise as 
your WorkingPrecision. In particular, if you are using machine 
precision number in your input  all this won't do you any good. You 
should really send your example otherwise it is hard to tell what you 
are really doing.

Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

• References:
  • Default Precision isn't reached yet no warning about convergence are generated
    • From: "Michael Beqq" <mbekkali@iastate.edu>