On Convergence Rates of Root-Seeking Methods

[emece67]

(03-14-2018 08:32 PM)Claudio L. Wrote:  For non-bracketed ones, secant, Newton and Steffensen (I need to research this one, first time I hear its name), seems fairly vanilla. Perhaps I'll add some of Namir's experiments with Ostrowski, Halley, etc. just to keep it interesting.

For non-bracketed methods, you may find this paper interesting. It compares up to 13 different non-bracketed methods (not high order, high complexity ones, the highest order method in the comparison is Ostrowsky-Traub, 4rd order), being Newton, Halley & Steffensen among them. On this paper, Steffensen method failed to converge many, many times (although the author works in the complex plane, not in the real line).

Also, the fractal pictures on the paper are nice :-)

Regards.