An efficient algorithm for the computation of a solution to von Neumann´s model

Abstract

The possibility of application of the van Neumann model was hampered by the non existence of an efficient algorithm for i ts solution. The essential difficulty lies in the fact that in general there is no solution in the rational field, solutions are related to high degree polynomial roots. Therefore, an iterative method is proposed permitting a rapid approximation to the solution by means of reiterated solutions of linear programming problems. Using the simplex method it is possible to solve rapidly the linear program in each step, thus obtaining the maximum rate of growth by a false position method.