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.