Considering iterative sequences that arise when the approximate solution $x_k$ to a numerical problem is updated by $x_{k+1} = x_k+v(x_k)$, where $v$ is a vector field, we derive necessary and sufficient conditions for such discrete methods to converge to a stationary point of $v$ at different Q-rates in terms of the differential properties of $v$ and in terms of the asymptotic dynamical behaviour of the associated continuous dynamical system.
Citation
Research report NA-04/10, Oxford University Computing Laboratory, May 2004