Several engineering applications need a robust method to find all the roots of a set
of nonlinear equations automatically. The proposed method guarantees monotonous convergence,
and it can determine whole submanifolds of the roots if the number of unknowns is
larger than the number of equations. The critical steps of the multidimensional bisection
method are described and possible solutions are proposed. An ecient computational
scheme is introduced. The eciency of the method is charac-terized by the box-counting
fractal dimension of the evaluated points. The multidimensional bisection method is
much more ef-ficient than the brute force method. The proposed method can also be
used to determine the fractal dimension of the submani-fold of the solutions with
satisfactory accuracy.
