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MathGroup Archive 2000

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Re: FixedPoint vs. FixedPointList

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24431] Re: [mg24384] FixedPoint vs. FixedPointList
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Tue, 18 Jul 2000 00:58:29 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Here is one (very standard) way illustrated with the well known example of
the function whose FixedPoint gives an approximate value of Sqrt[2]:

In[1]:=
sq[x_] := (x + 2/x)/2

In[2]:=
index = 0

In[3]:=
FixedPoint[(index++; sq[#]) &, 1.]
Out[3]=
1.41421

In[4]:=
index
Out[4]=
6

Andrzej

-- 
Andrzej Kozlowski
Toyama International University, JAPAN

For Mathematica related links and resources try:
<http://www.sstreams.com/Mathematica/>





on 7/13/00 12:13 PM, Otto Linsuain at linsuain+ at andrew.cmu.edu wrote:

> 
> Hi all. I need to know the fixed point of a function (to a certain
> accuracy) starting from a certain value of the arguement, say:
> 
> x = FixedPoint[ f, x, SameTest -> ( #2-#1 < somesmallnumber &) ]
> 
> I do not care about the intermediate results, but I would like to know
> how many iterations it takes for the process to converge. FixedPointList
> will do, for example:
> 
> {n,x}={Length[#],Last[#]}& @ FixedPointList[....]
> 
> However I believe this would cause problems. The reason is that x is
> really a very long list (FixedPoint works for lists too), and it could
> take many iterations for this to settle. Mathematica, I believe, stores
> only a maximum of two values at any given moment when executing
> FixedPoint, but it stores all intermediate values for FixedPointList,
> and most certainly would run out of memory.
> 
> Could any think of how to trick Mathematica to count the iteration
> without trying to store all the results?
> 
> Any suggestions would be greatly appreciated. Otto Linsuain.
> 




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