FindRoot vs. FindMinimum and Dedekind Eta Functions
- To: mathgroup at smc.vnet.net
- Subject: [mg102957] FindRoot vs. FindMinimum and Dedekind Eta Functions
- From: Ben Dundee <dundee at mps.ohio-state.edu>
- Date: Thu, 3 Sep 2009 05:38:44 -0400 (EDT)
Hello all!
I am having a strange problem with FindRoot, FindMinimum, and the Dedekind Eta function.
In short, I have a function that is proportional to the eta function to some power: DedekindEta[i t]^p, where p is an integer. I know (both from theory and graphing) that the minimum of the function should appear near t = 1.23... However, FindRoot finds the minimum at about 1.34..., an error of 10%! In other words, I evaluate FindRoot[ d_t f(t)==0,{t,123/100}], and get the wrong answer. (d_t is a derivative wrt t.) Now, I can do the same thing with FindMinimum, or NMinimize, and find the correct answer.
This bug seems to be independent of any values of the options in FindRoot. I have tried changing Precision and Accuracy values, using a different Method, and using the ``compiled'' option, all to no avail.
And it's not an issue of FindRoot finding the wrong root---the solution that FindRoot gives isn't a root at all!
My question is: has anyone else noticed a similar problem with Dedekind eta functions, and/or the FinRoot and FindMinimum commands?
I can't attach a copy of the notebook, so if anyone wants to see explicitly the problem I'm describing, email me and I'll send you the notebook (~78K).