On Convergence Rates of Root-Seeking Methods

[Claudio L.]

(03-11-2018 09:06 PM)Mike (Stgt) Wrote:  

(03-11-2018 02:26 PM)Claudio L. Wrote:  * Newton-Raphson

For all root finding functions on HP calculators I must only enter the function. Newton-Raphson needs also the first derivate of it, other methods need in addition the second derivate, some even higher derivates. Should the user enter them or will your planned sover find them on its own?

Ciao.....Mike

Almost every method has an implementation using some variant of difference formulae to replace the derivatives and come up with a workable algorithm. I'm not planning to reinvent the wheel, I'll research what's already being used and go with it. I even looked at some promising 16th order methods but I'm not so sure how tight is the convergence radius, it might need other methods to get the first few digits, then a few iterations of those methods can quickly give you a lot of digits.