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Re: why extending numbers by zeros instead of dropping precision is a good idea

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  Re: why extending numbers by zeros instead of dropping precision is a good idea Richard Fateman <fateman@cs.berkeley.edu> - 2011-04-07 12:06 +0000

#1520 — Re: why extending numbers by zeros instead of dropping precision is a good idea

On 4/4/2011 3:30 AM, Noqsi wrote:
> On Apr 1, 1:34 am, Bill Rowe<readn...@sbcglobal.net>  wrote:
>
>> It seems FixedPoint is doing something behind the scene that
>> avoids the problem you describe above.
>
> Well, of course, a specialized function can use specialized error
> estimation methods.
>

FixedPoint can be written in about one line.  It needs a stopping 
criterion, SameTest which in Mathematica can be any function you choose 
or the system's mysterious "automatic".  There is probably nothing much 
special in the default SameTest.  I expect it is something like

SameTest[x0_,x1_]:= Abs[(x1-x0)]  < Abs[x0]*10^(Precision[x0]) ;; we 
assume x0 is not zero; else use x1 on rhs; If they are both zero, 
obviously the fixed point has been reached...

  I suspect this test is best executed in fixed precision, but maybe it 
doesn't matter much.

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