A Bisection Method to Find All Solutions of a System of Nonlinear Equations

                             Petr Mejzl\'{\i}k
 
              Institute of Computer Science, Masaryk University
                  Buresova 20, 60200 Brno, Czech Republic
                             mejzlik@muni.cz

This paper describes an algorithm for the solution of a system of nonlinear 
equations F(x) = 0, where F = (f_1, ..., f_n): D \subset 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 finds 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.