A New Dimension-reducing Method for Solving Systems of Nonlinear Equations

A new method for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in Rn is presented. Firstly, 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 and subsequently it perturbs the corresponding Jacobian by using proper perturbation parameters. The remaining component of the solution is evaluated separately using the final approximations of the other components. This reduced iterative formula generates a sequence of points in Rn-' which converges quadratically to the 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.