Many data analysis problems in psychology may be posed conveniently in terms which place the parameters to be estimated on one side of an equation and an expression in these parameters on the other side. A rule for improving the rate of convergence of the iterative solution of such equations is developed and applied to four problems: the principal axis communality problem, individual differences multidimensional scaling, LP norm multiple regression, and LP norm factor analysis of a data matrix. The rule results in substantially faster solutions or in solutions where none would be possible without the rule.