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Re: FixedPoint[Cos, 1.0]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119365] Re: FixedPoint[Cos, 1.0]
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Wed, 1 Jun 2011 04:31:05 -0400 (EDT)
  • References: <is2kjq$qrm$1@smc.vnet.net> <4DE4EE6D.7010302@gmail.com>

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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