Newton and Halley's methods with enhanced derivatives estimation

[Dieter]

(10-06-2017 09:50 PM)Dieter Wrote:  It's the relative error that should be compared to this value. So the respective code line should better read

130 IF ABS(D)>=ABS(T*X) THEN 50

BTW, this may cause an infinite loop if X=0: in this case the test is always true. So at least the ">=" should be replaced with ">". Maybe someone has a better idea how to handle this case.

And FTR: with 0,1 for both initial guesses the 35s returns 0,0659646010297. If the final "–X–1" in the equation is changed to "–1–X" the result changes to 0,0659646009800. But as already mentioned there are multiple values around 0,065964601 for which the equation will evaluate to zero on a 12-digit calculator.

Dieter