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