BesselJZeros strangeness
- To: mathgroup@smc.vnet.net
- Subject: [mg12022] BesselJZeros strangeness
- From: "L. Dwynn Lafleur" <lafleur@usl.edu>
- Date: Fri, 17 Apr 1998 03:40:57 -0400
- Organization: University of Southwestern Louisiana
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. Consider the following cells cut-and-pasted from a notebook. -------------------- (* 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. Would someone more experienced with Mathematica than I please explain this behavior? Thanks. Dwynn -- ============================================== L. Dwynn Lafleur Professor of Physics The University of Southwestern Louisiana Lafayette, Louisiana (USA) lafleur@usl.edu ==============================================