 Order of convergence

An iteration converging to $x_{\ast }$ has exact asymptotic order $p$ if its nonzero errors $e_k=x_k-x_{\ast }$ satisfy the displayed limit. A bound $\Vert e_{k+1}\Vert \le C\Vert e_k{\Vert }^p$ instead asserts at least order $p$. Finite termination is treated separately because the error ratios become undefined.