Machine arithmetics Q?

*To*: mathgroup at smc.vnet.net*Subject*: [mg3657] Machine arithmetics Q?*From*: "Arturas Acus" <acus at itpa.lt>*Date*: Tue, 2 Apr 1996 21:55:09 -0500*Comments*: Authenticated sender is <acus@mserv.itpa.lt>*Sender*: owner-wri-mathgroup at wolfram.com

Hello, It is known, that following two formulas give the same result. sinusas[i_]:=sinusas[i]=N[Sin[2^i*ArcSin[Sqrt[x0]]]^2,prec]; iter[i_]:=iter[i]=4*iter[i-1]*(1-iter[i-1]); I want to demonstrate, that we must calculate correct. That is, if we use $MachinePrecision numbers after some steps we will get random numbers: prec=5;maximum=100; iter[0]=x0=N[1/3,prec]; deltalist=ListPlot[Table[ N[(sinusas[i]-iter[i]),prec],{i,maximum}]] This result is ok., because we have positive and negative differences in calculations. Now I want to show, that if we will use 20 digits, and machine arithmetic (Not Big Numbers Arithmetic !) we will get chaos later. Therefore I remove Big Numbers Arithmetic: $MinPrecision=$MaxPrecision=20; prec=20; and perform the same calculations. What I get is quite different! After some iterations I get only negative deviations! Can anybody explain why this happens? I use Mathematica 2.2.1 for Windows. Thanks in advise Arturas Acus E-mail: acus at itpal.lt Institute of Theoretical Physics and Astronomy, Gostauto 12, 2600, Vilnius, Lithuania. ==== [MESSAGE SEPARATOR] ====