That's one sophisticated root-finding algorithm! Henry has evidently researched Henrici's algorithm more thoroughly than I --- but my recollection is that there's no connection. WFL On 9/16/10, Victor Miller <victorsmiller@gmail.com> wrote:
How is it related to Schonhage's splitting circle method? http://en.wikipedia.org/wiki/Splitting_circle_method
Victor
On Thu, Sep 16, 2010 at 1:29 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
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
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