Re: Plotting with arbitary precision????

*To*: mathgroup at smc.vnet.net*Subject*: [mg69616] Re: [mg69611] Plotting with arbitary precision????*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 17 Sep 2006 22:45:48 -0400 (EDT)*Reply-to*: hanlonr at cox.net

Needs["Calculus`Pade`"]; ratApp[x_] = Pade[Exp[x], {x, 0, 12, 12}] // Together; relErr[x_?NumberQ, prec_:50] := Module[ {xp = SetPrecision[x, prec]}, (ratApp[xp] - Exp[xp])/Exp[xp]]; Plot[10^22*relErr[x], {x, -2.5, 2.5}, PlotRange -> All, Frame -> True, Axes -> False, ImageSize -> 400]; Bob Hanlon ---- lcw1964 <leslie.wright at alumni.uwo.ca> wrote: > 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 >