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MathGroup Archive 1998

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Re: BesselJZeros strangeness



> I am using Mathematica 3.0.1 in Windows 95.  I obtain rather strange (at
> least, to me) results when using the BesselJZeros function in the
> NumericalMath`BesselZeros` package.
>
> In[1]:= << NumericalMath`BesselZeros`
>
> In[2]:= BesselJZeros[0, 5]
>
> Out[2]= $Aborted
>
> (*  Above aborted after about 3 minutes of no output  *)
>
> In[3]:= BesselJZeros[0, 5, AccuracyGoal->8]
>
> Out[3]= {2.40483,5.52008,8.65373,11.7915,14.9309}
>
> (*  Above output appears in much less than one second  *)
>
> Would someone more experienced with Mathematica than I please explain
> this behavior?  Thanks.

This is a problem in machine-number evaluation of BesselJ in Mathematica
Version 3.0.1 for Windows.  I do not believe there are any other
affected versions.  I don't know if the problem is in Mathematica or in
Windows, and I suppose it doesn't matter.  The solution is to avoid
machine numbers, or to otherwise adjust the way numerical errors work
out in the calculation. For more information see the Wolfram Research
web site (http://www.wolfram.com/
support/Kernel/Symbols/NumericalMath/BesselZeros/BesselJZeros.html). 
All of these examples will finish in a few seconds if you avoid machine
numbers.

Dave Withoff
Wolfram Research



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