On Convergence Rates of Root-Seeking Methods

[JurgenRo]

(01-30-2017 10:06 PM)emece67 Wrote:  Thanks a lot, Namir, for your work.

I was also a bit shocked when the convergence orders I computed were usually lower than the expected ones. After some trials I assumed that I was working with too many digits. If, for example, one is working with 10 digits & with a 4th order method that, supposedly, multiplies the number of correct digits by 4 on each iteration (provided the method is actually converging to a root), you will only see such order if your guess has 2 or 3 correct figures. If the guess has less correct figures the method is not yet converging and does not show the expected convergence rate, if your guess has more that those correct figures, then the method cannot show such order because it "exhausts" all available digits (I think this is the reason for you not seeing the expected order in the last iterations).

I was, at last, able to see the theoretical convergence orders when I switched to 1024 digits.

Regards.

Convergene rate dependents on the numbers of Digits used? Mmmh ...