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RE: Plot, Cursor and Spelling Errors questions


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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