Locating three-dimensional roots by a bisection method (Q1184614)

This paper considers the evaluation of roots of a system of equations. Bisection methods for finding roots of equations have certain distinct advantages, particularly in their stability. They depend on the existence of a criterion for determining whether a root exists within a given volume. This paper exploits the topological degree theory to provide this criterion by which one can test if there is a null within a given volume. Only three-dimensional volumes are considered. The result is used in locating roots and in illustrating the theory. The classification of roots as \(X\)-points or \(O\)-points and its generalization to three dimensions are also discussed.