Nonstationary model solution techniques and the USA algorithm: Some practical experience

A variety of iterative techniques are available for solving large, sparse, nonlinear equation systems. This paper reviews first-order, nonstationary iterations which automatically accelerate convergence. In particular, we compare automatic Fast Gauss-Seidel methods, the USA algorithm, and fixed parameter Fast Gauss-Seidel iterations for solving large-scale, nonlinear macroeconomic models. Attention is drawn to their robustness properties and computational costs. On both grounds, the USA algorithm is found to compare unfavourably for a selection of five models of the UK economy. That effectively invalidates the USA algorithm as a method for solving macroeconomic models.