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Groups > comp.soft-sys.math.mathematica > #2848

Re: FixedPoint[Cos, 1.0]

From Szabolcs Horvát <szhorvat@gmail.com>
Newsgroups comp.soft-sys.math.mathematica
Subject Re: FixedPoint[Cos, 1.0]
Date 2011-06-01 08:30 +0000
Organization Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID <is4tc3$b01$1@smc.vnet.net> (permalink)
References <is2kjq$qrm$1@smc.vnet.net> <4DE4EE6D.7010302@gmail.com>

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On 2011.05.31. 15:34, Szabolcs Horvát wrote:
> On 2011.05.31. 13:49, J Siehler wrote:
>> My numerical analysis students this past term pointed out to me that
>> the command
>>
>> FixedPoint[Cos, 1.0]
>>
>> which is the first example in the Information for FixedPoint doesn't
>> ever finish running (or, not in any reasonable amount of time). We
>> tried this on serveral versions of Mathematica (6.x, 7.x, and 8.x),
>> all on OS X, and got the same nonresult.
>>
>> It can be forced by specifying something like FixedPoint[Cos, 1.0,
>> SameTest -> (Abs[#1 - #2]< 10^-10&)] or FixedPoint[Cos, 1.0, 40],
>> but it seems like that should be unnecessary, and the form given in
>> the documentation should work. Can anybody else confirm this
>> behavior? Am I missing something totally obvious here?
>>
>
> On Windows / Pentium M it finishes if I pass a machine number (1.0) to
> it. It does not finish if I pass it a number with fixed precision (e.g.
> 1.0`10) because the Precision of the result keeps increasing with
> successive applications of Cos.
>
> I'm curious, on your machine will the function keep oscillating between
> two values? What (and how many) values do you get if you do e.g.
>
> Union@Take[Length@FixedPointList[Cos, 1.0, 1000], -10]
>

Sorry, of course I mean

Union@Take[FixedPointList[Cos, 1.0, 1000], -10]

!

I seem to get a similar behaviour on my machine with another function:

Cos[#]^2 &

Doing

Union@Take[FixedPointList[Cos[#]^2&, 1.0, 1000], -10]

shows that it's indeed oscillating between two values.

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Thread

FixedPoint[Cos, 1.0] J Siehler <jsiehler@gmail.com> - 2011-05-31 11:49 +0000
  Re: FixedPoint[Cos, 1.0] David Reiss <dbreiss@gmail.com> - 2011-06-01 08:30 +0000
  Re: FixedPoint[Cos, 1.0] Szabolcs Horvát <szhorvat@gmail.com> - 2011-06-01 08:30 +0000
  Re: FixedPoint[Cos, 1.0] Szabolcs Horvát <szhorvat@gmail.com> - 2011-06-01 08:30 +0000
  Re: FixedPoint[Cos, 1.0] "Dr. Wolfgang Hintze" <weh@snafu.de> - 2011-06-01 08:32 +0000
  Re: FixedPoint[Cos, 1.0] Erik Max Francis <max@alcyone.com> - 2011-06-01 08:32 +0000

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