Locating three-dimensional roots by a bisection method

Bisection methods, which depend on the existence of a criterion for determining whether a root exists within a given volume, may be useful in the evaluation of equation roots since the volume in which the root is known to be located can be steadily decreased. This criterion is presently furnished via topological degree theory, strictly for the case of 3D volumes; usefulness is demonstrated in the location of roots, and the classification of roots as either X- or O-points is discussed.