Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1998
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1998

[Date Index] [Thread Index] [Author Index]

Search the Archive

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
____________________________________________________________________



  • Prev by Date: Re: How to plot list from (0,0) ?
  • Next by Date: Re: Pattern matching more than once
  • Prev by thread: Re: BesselJZeros strangeness
  • Next by thread: Subscription and hamiltonian.