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MathGroup Archive 2006

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Plotting with arbitary precision????

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69611] Plotting with arbitary precision????
  • From: "lcw1964" <leslie.wright at alumni.uwo.ca>
  • Date: Sun, 17 Sep 2006 06:58:06 -0400 (EDT)

Hi there,

I am a long time user of another system who has been given the chance
to try out Mathematica 5.2, and I must admit in some regards I like it
better, though it handles floating point computation (which I am most
interested in) in a way that takes some getting used to for me.

I am using the MiniMaxApproximation routine in the Numerical Math package,
and am interested in generating error curves from the results.  I have
figured out how to invoke arbitrary precision in the MiniMaxApproximation
routine with the WorkingPrecision option, so I am not confined to
Machine Precision.

However, the problem comes with the plotting. In a very good rational
approximation for Exp[x] I have a maximum relative error of, say, about
10^-22. Let's call it RatApp. If I try to plot (RatApp-Exp[x])/Exp[x]
on my interval of approximation, I don't get a nice smooth double
ripple error curve like I should. I get a noisy mess confined to
about +/- 10^-17. Which is precisely what I should get since Plot uses
only machine precision (not the 30 or so digits of arbitary working
precision specified) when generating plots. Since the numerator of my
error function will differ only in the 22nd digit or so and beyond,
the subtlety of the subtraction is lost.

Online help for Plot doesn't seem to provide an arbitrary precision
"override" to get over this issue. In the other system, one simply had
to increase the Digits setting since everything is done in software
floating point anyway--slower, but easier to use. Is there any way in
Mathematica to plot a function that requires such high precision in
interim calculations so that the plot is accurate?

Many thanks in advance,

Les


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