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Several engineering applications need a robust method to find allthe roots of a set of nonlinear equations automatically. The proposed methodguarantees monotonous convergence, and it can determine whole submanifoldsof the roots if the number of unknowns is larger than the number ofequations. The critical steps of the multidimensional bisection method aredescribed and possible solutions are proposed. An efficient computationalscheme is introduced. The efficiency of the method is characterized by thebox-counting fractal dimension of the evaluated points. The multidimensionalbisection method is much more efficient than the brute force method. Theproposed method can also be used to determine the fractal dimension of thesubmanifold of the solutions with satisfactory accuracy.

Bisection method in higher dimensions and the efficiency number