Acceleration by aggregation of successive approximation methods

Methods of successive approximation for solving linear systems or minimization problems are accelerated by aggregation-disaggregation processes. These processes, which modify the iterates being produced, are characterized by a two directional flow of information between the original higher dimensional problem and a lower dimensional aggregated version. This technique is characterized by means of Galerkin approximations, and this in turn permits analysis of the method. A deterministic as well as probabilistic analysis is given of a number of specific aggregation-disaggregation examples. Numerical experiments have been performed, and these confirm the analysis and demonstrate the acceleration. © 1982.