[Proj] Re: Dozier's TM method---my summary

[Oscar van Vlijmen]

> From: "Gerald I. Evenden"

> Stating it another way, my surrender was to the Dozier article that while the
> method sounds interesting the execution falls short.  The code had several
> errors and some methodology is in question.  I have spent an additional week
> rooting out a complex Bulirsch routine from the old Bell lab site and spent
> several days relating Jacobi's form to Legendre in order to test against
> Abramowitz tables and GSL software for at least real arguments---they now
> agree.  But Dozier's code does not agree to better than the third or forth
> place (I am not saying Dozier's code is wrong yet).
> 
> And I still have no handle on a replacement for Newton-Raphson.

What surprises me is that I gave an alternative twice, once in a posting on
this list dated 2006-06-13, once in a private email dated 2006-06-23,
including a web reference.
It's about ACM TOMS algorithm 365 from H. Bach. Fortran code can be found at
netlib.org and one can buy a copy of the peer reviewed TOMS article at ACM
(acm.org).
I am not happy with the method because it is horribly slow, but it is a very
robust method, at least if one knows how to tweak its control parameters.

As for a replacement of complex Jacobi elliptic functions and a complex
elliptic integral: it can be done without too much effort. I provided in the
same manner (list posting and private email) references.
I do admit that working with complex elliptics is no trivial endeavor
without knowledge or experience.