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MathGroup Archive 2005

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Re: FixedPoint stops "when elements no longer change"?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62808] Re: FixedPoint stops "when elements no longer change"?
  • From: dh <dh at metrohm.ch>
  • Date: Mon, 5 Dec 2005 13:41:25 -0500 (EST)
  • References: <dn0v44$8ge$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Steven,
to see all decimal places you could say:

NumberForm[#, 17] & /@ FixedPointList[Cos, 1.0]

Daniel

Steven T. Hatton wrote:
> This is the example in The Mathematica Book for FixedPointList:
> 
> FixedPointList[Cos, 1.0]
> 
> {1., 0.540302, 0.857553, 0.65429, 0.79348, 0.701369, 0.76396, 0.722102, \
> 0.750418, 0.731404, 0.744237, 0.735605, 0.741425, 0.737507, 0.740147, \
> 0.738369, 0.739567, 0.73876, 0.739304, 0.738938, 0.739184, 0.739018,
> 0.73913, \
> 0.739055, 0.739106, 0.739071, 0.739094, 0.739079, 0.739089, 0.739082, \
> 0.739087, 0.739084, 0.739086, 0.739085, 0.739086, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085}
> 
> A bit of poking around showed me that this is using SameQ for SameTest.
> 
> "SameQ requires exact correspondence between expressions, except that it
> considers Real numbers equal if their difference is less than the
> uncertainty of either of them."
> 
> I guess I'm not seeing all the decimal places used to generate to list
> above.  How would I determine the precision used to determine two
> successive values are unchanged?
> 
> I tried FixedPointList[N[Cos[#], 2] &, 1.0], but that changed neither the
> display, nor the result. 


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