# -*- 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.