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MathGroup Archive 1998

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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


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