A NEW DIMENSION - REDUCING METHOD FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

A new method for the numerical solution of systems of nonlinear algebr aic and/or transcendental equations in R(n) is presented. Firstly, thi s method reduces the dimensionality of the system in such a way that i t can lead to an iterative approximate formula for the computation of n-1 components of the solution and subsequently it perturbs the corres ponding Jacobian by using proper perturbation parameters. The remainin g component of the solution is evaluated separately using the final ap proximations of the other components. This reduced iterative formula g enerates a sequence of points in R(n-1) 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 prob lems with imprecise function values. A proof of convergence is given a nd numerical applications are presented.