Several iterative procedures have previously been developed for the numerical solution of polynomial equations. Some methods may require more work for each step than others, but in return each step gives a greater improvement of the current estimate. The algebraic complexity of a method is a measure that takes these two factors into account and may serve as a guide for choosing between competing methods to solve a given equation. The author shows that, when certain assumptions are satisfied, 1-point methods are most efficient. The treatment is general and is applicable to polynomials whose coefficients belong to an arbitrary field. Illustrations with the usual Newton iteration and Regula falsi are provided. This paper is of most interest to specialists in algebraic complexity. The reference list is adequate.