I have a sequence of points which was obtained from an iterative algorithm, and I computed the order of convergence $p$ of the method using the formula
$$ p \approx \frac{\log({\rm err}(k+2))-\log({\rm err}(k+1))}{\log({\rm err}(k+1)) - \log({\rm err}(k))}. $$
The first computed ratio is much larger compared to the other ones. Without removing this value from the complete list of values, I obtained $p = 1.2615$ as the order of convergence of my algorithm. However, when I computed the order of convergence after removing the outlier (the first calculated ratio), I got $p = 1.0495$ (see figure).
My question is, which of the two is the correct order of convergence of my algorithm?
1.0495
value more likely to be correct. $\endgroup$ – Nox Jan 29 '19 at 14:02