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This paper describes an algorithm for the solution of a system of nonlinear equations F(x) = , where F = (f 1 ; : :: ; fn) : D R m ! R n and D is a compact domain, given that any of the functions f i is monotonic when restricted to any single variable at an arbitrary point. The algorithm nds an approximation of the solutions as a union of m{dimensional intervals. The computation is based on reduction of the box containing all the solutions, its bisection, and elimination of subintervals which do not contain a solution. The algorithm does not require computation of partial derivatives or their approximations. Its use is illustrated on a model case.

A bisection method to find all solutions of a system of nonlinear equations