Re: FixedPoint[Cos, 1.0]

*To*: mathgroup at smc.vnet.net*Subject*: [mg119558] Re: FixedPoint[Cos, 1.0]*From*: Dana DeLouis <dana01 at me.com>*Date*: Thu, 9 Jun 2011 05:46:22 -0400 (EDT)

> My numerical analysis students this past term As a silly side note, the Newton version of the equation Cos[x]=x did a little better by getting to a number ending in 606. We're looking for a number ending in 607. Cos[.7390851332151607] 0.7390851332151607` Newton[Cos[x]-x, x] (Cos[g]+g Sin[g])/(1+Sin[g]) fp[g_]=%; FixedPointList[fp,1.0] { 1.`, 0.7503638678402439`, 0.7391128909113617`, 0.7390851333852838`, 0.7390851332151607`, 0.7390851332151606` } = = = = = = = = = = : >) Dana DeLouis $Version 8.0 for Mac OS X x86 (64-bit) (November 6, 2010) On May 31, 7:49 am, J Siehler <jsieh... at gmail.com> 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?