On Convergence Rates of Root-Seeking Methods

[Dieter]

(03-08-2018 05:35 AM)Gamo Wrote:  I'm new to this subject and I found this subject is very interesting.

First of all: the original post by Namir indeed was about root-seeking methods, i.e. methods for solving f(x)=0. But the last posts deal with a different topic, they are about methods for calculating square roots of a number.

(03-08-2018 05:35 AM)Gamo Wrote:  I happen to try other program that use "Regula Falsi method"
I try on 11C this method is much faster than the Newton's Method with this Regula Falsi program you need to provide reference points to X1 and X2 while providing the reference point this can be check right away if that two points is far apart or not when done give it the tolerant and start to compute when done can check for the accuracy against 0 value.

Wow, that was quite a long sentence. Even without a single period or comma. ;-)

Anyway, the Newton method usually is converging with a similar speed as Regula Falsi and its variants. But the latter has the advantage that the user can provide two guesses that bracket the solution. It may be faster here and there because each iteration only requires one call of f(x) instead of two for the Newton method (f(x) and f(x+h) or f(x) and f'(x)).

BTW, Gamo, I just noticed the PM you sent a few days ago. I now sent a reply – and an 11C program. ;-)

Dieter