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# Re: BesselJZeros strangeness
*To*: mathgroup@smc.vnet.net
*Subject*: [mg12076] Re: BesselJZeros strangeness
*From*: Paul Abbott <paul@physics.uwa.edu.au>
*Date*: Sat, 25 Apr 1998 01:30:12 -0400
*Organization*: University of Western Australia
*References*: <6h7564$m8@smc.vnet.net>
L. Dwynn Lafleur wrote:
> 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.
>
> (* First two input cells are from Mathematica 3.0 help file describing
> 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 *) In[4]:= BesselJZeros[0, 2]
> Out[4]= {2.40483,5.52008}
> In[5]:= BesselJZeros[0, 3]
> Out[5]= $Aborted
> In[6]:= BesselJZeros[0, 6]
> Out[6]= $Aborted
> In[7]:= BesselJZeros[0, 7]
> Out[7]= {2.40483,5.52008,8.65373,11.7915,14.9309,18.0711,21.2116}
> In[8]:= BesselJZeros[0, 20]
> Out[8]= {2.40483,5.52008,8.65373,11.7915,14.9309,18.0711,21.2116,24.3525,27.4935,
> 30.6346,33.7758,36.9171,40.0584,43.1998,46.3412,49.4826,52.6241,55.7655,
> 58.907,62.0485}
> ---------------------
> Note that, contrary to what is suggested in the help file, BesselJZeros
> cannot calculate the first 5 zeros unless an AccuracyGoal setting is
> explicitly stated. This particular resulty is strange since the
> default options for BesselJZeros are {WorkingPrecision->16,
> AccuracyGoal->Automatic}, and according to the Mathematica
> documentation, the Automatic setting for AccuracyGoal sets it to 10
> fewer digits than WorkingPrecision, i.e. 6. However, AccuracyGoal->8
> works while the default does not.
>
> We also see that BesselJZeros can be called to calculate the first 2
> zeros but not the first 3 zeros or the first 6 zeros. However, it can
> calculate the first 7 zeros and the first 20 zeros.
This is rather puzzling. On a Macintosh
In[1]:= << NumericalMath`BesselZeros`
In[2]:= Table[BesselJZeros[0, n],{n,2,7}]//Timing
Out[2]= {3.31667 Second,
{{2.40483,5.52008},{2.40483,5.52008,8.65373},{2.40483,5.52008,
8.65373,11.7915},{2.40483,5.52008,8.65373,11.7915,14.9309},{2.40483,
5.52008,8.65373,11.7915,14.9309,18.0711},{2.40483,5.52008,8.65373,
11.7915,14.9309,18.0711,21.2116}}}
or under Mathematica 3.0 for Linux
In[1]:= << NumericalMath`BesselZeros`
In[2]:= Table[BesselJZeros[0, n],{n,2,7}]//Timing
Out[2]= {2.47 Second, {{2.40483, 5.52008}, {2.40483, 5.52008, 8.65373},
> {2.40483, 5.52008, 8.65373, 11.7915},
> {2.40483, 5.52008, 8.65373, 11.7915, 14.9309},
> {2.40483, 5.52008, 8.65373, 11.7915, 14.9309, 18.0711},
> {2.40483, 5.52008, 8.65373, 11.7915, 14.9309, 18.0711, 21.2116}}}
there is no problem.
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul@physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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