| Author |
Comment/Response |
Bill Simpson
|
 10/09/12 12:22pm
I believe you are exhausting the ~16 digits of $MachinePrecision and your loop exits at about that iteration for any threshold smaller than 10^-$MachinePrecision.
As an experiment I chanced all your coefficients to have 32 digits of precision, set the threshold at 1.0`32*^-24 and modified your diagnostic messages to tell how many times ConvergenceCount was set to zero on each pass. This then gives
From In[1]:= ConvergenceLoop=0 ConvergenceCount=0
From In[1]:= ConvergenceLoop=100 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=200 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=300 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=400 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=500 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=600 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=700 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=800 ConvergenceCount=2048
From In[1]:= ConvergenceLoop=900 ConvergenceCount=498
From In[1]:= ConvergenceLoop=908
From In[1]:= Convergence Loop Limit Not Reached.
From In[1]:= 908 Congratulations Converged!
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