Stability of Difference Equations and Convergence of Iterative Processes

In this report, we review several connections between the theory of convergence of iterative processes and the theory of Lyapunov stability of ordinary difference equations. Among the topics discussed are local convergence and asymptotic stability, global convergence and global asymptotic stability, Lyapunov functions, domain of attraction, total stability and rounding errors, nonautonomous equations and variable operator iterations.