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Re: Increased Precision in Plot?


> The command
> 
> f[t_]=Nest[1 - Integrate[2s(#/.t->s),{s, 0, t}]&, Cos[t],
> 12]//Simplify
> 
> returns a fairly innocent-looking result. However, evaluation (or
> plotting) of the result with default precision produces garbage; for
> example:
> 
> In[1]:= f[.5]
> Out[1]:= 0.875
> 
> In[2]:= N[f[1/2]]
> Out[2]:= 0.625
> 
> In[3]:= N[f[1/2],17]
> Out[3]:= 0.77880078307140487
> 
> My question is this: How can I get Plot to graph such a function with
> increased precision, so that the graph isn't overwhelmed by noise?
> 
> Thanks in advance,
> 
> Selwyn Hollis

Here is one possibility:

Plot[Block[{tt = SetPrecision[t, 100]}, f[tt]],
    {t, 0, 1}, Compiled -> False]

which could be compared with Plot[f[t], {t, 0, 1}] to see the effect.
There are many variants of this.  It has been suggested that since
Plot is essentially a numerical function (like NIntegrate) it could
have a WorkingPrecision option, which would provide another way of
addressing this issue.

Dave Withoff
Wolfram Research


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