# -*- org -*-
#+CATEGORY: complex

* Complex polynomial solvers (Got Newton-Mueller from
jotahtin@cc.hut.fi, still to add (BJG)).

* The asymptotic behavior of the secondary functions (sec, csc, cot,
etc) can overflow because of expressions like cosh(x) / D , where D =
cosh^2 which is computed prior to the division.  This should by
special casing "small" vs "large" arguments as has been done for the
sin,cos,tan versions.

* Perhaps there is something useful in LCY65 L. A. Lyusternik,
O. A. Chervonenkis, and A. R. Yanpol'skii, Handbook for computing
elementary functions, International Series of Monographs in Pure and
Applied Mathematics, vol. 76, Pergamon Press, Oxford, 1965.

* Comparing the Complex Arithmetic routines in Section 5.5 of Numerical Recipes 
gsl_complex_div() uses simple complex division while 5.5.5 has a more
sophisticated one that avoids underflow/overflow.