EFFICIENT UNIVARIATE METHOD TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS

An algorithm has been devised for the solution of a non-linear system of n equations in n unknowns. It consists in n2 unidimensional searches of a root followed by an acceleration step per iteration. The univariate searches locate n points on the hipersurface that represents each equation in the n-dimensional space. Those points are used to approximate linearly each equation. The intersection of the n hiperplanes gives a better approximation to the solution. Each iteration requires n2 univariate searches plus the solution of a linear system of dimension n - 1. Four alternatives for the practical application of the algorithm are described in the paper. The method has been applied to several problems in Chemical Engineering with dimensionality ranging from n = 2 to n = 6. Its efficiency has shown to be better than other methods currently in use. © 1979.