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