On Convergence Rates of Root-Seeking Methods

[emece67]

(03-18-2018 05:52 AM)Mike (Stgt) Wrote:  May be you are right, may be I am wrong, but the lucky choice of a good initial estimate is not reflected in your formula.

Sure, that is for I said this:

(03-17-2018 11:59 PM)emece67 Wrote:  Suppose we want to estimate the time needed for a root seeking algorithm to polish a root estimation [...]

With "polish" I want to mean that we are near (or very near) the root, so the algorithm can show its convergence order and it will enlarge the number of correct digits in the estimation. With 0 correct digits we are not near the root, my reasoning does not apply in such conditions.

And:

(03-17-2018 11:59 PM)emece67 Wrote:  Also, note that the time required for the algorithm for getting from a "distant" root estimation to the vicinity of the root (where the algorithm will start to show its convergence order) is not at all easily predictable from the convergence order, thus the valuable information on Varona's paper.

Where I want to mean that the order of convergence is not useful as a "speed" measure during this phase of the iterations.

Thus, my point is that the order of convergence is not useful at all to predict the "speed" of a iterative non-bracketing algorithm, neither far from the root nor converging into it.

Regards.