A new dimension-reducing method for solving systems of nonlinear equations

A method for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in 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−1)-dimensional iterative formula generates a sequence of points in 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.

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