On Convergence Rates of Root-Seeking Methods

[Dieter]

(03-11-2018 02:26 PM)Claudio L. Wrote:  Based on the tests reported in this thread, what methods would be a "must have" in each category?

Bracketed:
* Bisection
<add others here!>

I'd say that a (modifided) Secant / Regula Falsi method is a must here. The respective Wikipedia article has the two most common variants, the German version adds a third one. Among these the Illinois method has been used in several HP software pacs of the Seventies (cf. HP65 and HP41 Standard Pac).

Pauli may add a few more sophisticated methods, e.g. Brent's – I remember the discussion years ago with regard to the WP34s solver.

Dieter