Order of convergence
= Order of convergence
{title2=$\lim_{k\to\infty}\|e_{k+1}\|/\|e_k\|^p=C\in(0,\infty)$}
An iteration converging to $x_*$ has exact asymptotic order $p$ if its nonzero errors $e_k=x_k-x_*$ satisfy the displayed limit. A bound $\|e_{k+1}\|\leq C\|e_k\|^p$ instead asserts at least order $p$. Finite termination is treated separately because the error ratios become undefined.