Some Practical Aspects of Overrelaxation in Diagnostic and Forecast Calculations

If the conditions for the existence of a unique optimum overrelaxation factor are satisfied in a jury problem, then component suppression is a useful aid. In jury-marching forecast models, there is no unique optimum overrelaxation factor, because the error vector at acceptance is not dominated by the eigenvector corresponding to the spectral radius. The criterion for fewest iterations is not then the minimization of the spectral radius. It is advantageous to decrease the overrelaxation factor in a predetermined manner during the first two or three time steps or after component suppression. Theoretical results are derived to explain the original purely empirical observations that the coefficient which minimizes the spectral radius requires about 50 percent more computing time than is necessary.