Re: Re: Plot, Cursor and Spelling Errors questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg14495] Re: [mg14437] Re: [mg14393] Plot, Cursor and Spelling Errors questions*From*: Garrett Tim Sos <gts at mindspring.com>*Date*: Fri, 23 Oct 1998 20:59:14 -0400*References*: <199810210732.DAA14854@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Define garbage. Yes it worked on Mac 7100/66 just fine. As n is increased to 15, the difference (error) you plotted is reduced to something on the order of 10 ^ -16. On a 7100/66: $MachineEpsilon gives the smallest machine-precision number which can be added to 1.0 to give a result that is distinguishable from 1.0. Attributes[$MachineEpsilon] = {Protected} $MachineEpsilon = 2.220446049250313*^-16 Sounds about right. It appears that InterpolatingPolynomial uses machine-precision numbers. I did not investigate if this can be overridden. Tim Ranko Bojanic wrote: > > ... > > n = 15; > f[x_] := Exp[x]; > xLst = Table[Cos[((2*k - 1)*Pi)/(2*n)], {k, 1, n}]//Reverse; yLst = > N[Map[f,xLst], 30]; > fLst = Transpose[{xLst, yLst}]; > p[x_] := InterpolatingPolynomial[fLst, x]; Plot[Evaluate[f[x]-p[x]], {x, > -1, 1}, PlotPoints -> 50]; > > (with the last line corrected) and everything worked fine? Which > computer did you use? How did you configure Plot? > > On my computer (Power Macintosh 7500/100, with Mathematica 30.1) this > program produces garbage. > > Regards, > Ranko

**References**:**Re: Plot, Cursor and Spelling Errors questions***From:*Ranko Bojanic <bojanic@math.ohio-state.edu>