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RE: Plot, Cursor and Spelling Errors questions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg14450] RE: [mg14393] Plot, Cursor and Spelling Errors questions
*From*: Ranko Bojanic <bojanic at math.ohio-state.edu>
*Date*: Wed, 21 Oct 1998 03:32:47 -0400
*Organization*: Ohio State University
*Sender*: owner-wri-mathgroup at wolfram.com
Hi Ted!
Thanks for your suggestions. This problem of plotting curves whose
magnitude is smaller than the machine precision has bothered me for
many years while I was writing a Pascal program for the construction of
polynomials of best approximation to continuous function. If you have a
Macintosh computer, see Remez68K.sea.hqx or RemezPPC.sea.hqx at
fttp://ftp.math.ohio-state.edu/pub/users/bojanic or look for Remez at
http://archives.math.utk.edu/
software/mac/numericalAnalysis/.directory.html The program I posted is
just the first step in the construction of the polynomial of best
approximation to Exp[x] on [-1,1], of degree 14. If you want a
polynomial of degree 30, set n=31 and the precision 50 istead of 17
since the magnitude of the error curve is 10^(-42). The PrecisionPlot
module works fine in this case as well.
I still do not understand why anh how your module works.
PrecisionPlot[f_,{x_,xmin_,xmax_},opts___?OptionQ]/;
Head[f]=!=List:=
Module[{g,h},
g=Evaluate[f/.x->#]&;
h=g[SetPrecision[#,17]]&;
Plot[h[x],{x,xmin,xmax}, opts]
]
If you write a simpler module along these lines just to evaluate a
function f at a poin a with p decimal digits, you may write
eval[f_,a_,p_]:= Module[{g,h,x},
g=Evaluate[f[x]/.x->#]&;
h=g[SetPrecision[#,p]]&;
Return[h[a]]]
This gives
In[1] := eval[Exp,2.3, 30]
Out [1] = 9.9741824548147189681868930533
It looks like we can evaluate Exp[2.3] with arbitrary precision. But
In[2] := N[Exp[23/10],30]
Out[1] = 9.9741824548147207399576151569
gives a different result.
Thanks again for your help.
Ranko
Ranko Bojanic
bojanic at math.ohio-state.edu
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