16 Sep
2010
16 Sep
'10
11:29 a.m.
On 9/16/10, Joerg Arndt <arndt@jjj.de> wrote:
... This may not be what you have in mind but there are methods to find _all_ roots simultaneously, see e.g. http://en.wikipedia.org/wiki/Durand-Kerner_method and the references at the bottom of the page
A very elegant method which computes all roots simultaneously, yielding circles in which they are guaranteed to lie, is buried (I don't remember exactly where --- anybody else know?) in the strangely neglected Henrici P., Applied and Computational Complex Analysis (Wiley). [Three volumes: 1974, 1977, 1986.] It's interesting that these methods actually gain in speed and stability by simultaneity, as opposed to attempting to exclude the other roots. WFL