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.