A DIMENSION-REDUCING METHOD FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS IN RN

A method for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in [formula omitted] is presented. This method reduces the dimensionality of the system in such a way that it can lead to an iterative approximate formula for the computation of n— 1 components of the solution. while the remaining component of the solution is evaluated separately using the final approximations of the other components. This (n 11-dimensional iterative formula generates a sequence of points in [formula omitted] which converges quadratically to n-1 components of the solution. Moreover, it does not require a good initial guess for one component of the solution and it does not directly perform function evaluations, thus it can be applied to problems with imprecise function values. A proof of convergence is given and numerical applications are presented. © 1990, Taylor & Francis Group, LLC. All rights reserved.