Always convergent methods for nonlinear equations of several variables

We develop always convergent methods for solving nonlinear equations of the form f (x ) =0 ( f:ℝ^n→ℝ^m , x∈ B=× _i=1^n [ a_i,b_i ] ) under the assumption that f is continuous on B . The suggested methods use continuous space curves lying in the rectangle B and have a kind of monotone convergence to the nearest zero on the given curve, if it exists, or the iterations leave the region in a finite number of steps. The selection of space curves is also investigated. The numerical test results indicate the feasibility and limitations of the suggested methods.