LOCATING 3-DIMENSIONAL ROOTS BY A BISECTION METHOD

The evaluation of roots of equations is a problem of perennial interest. Bisection methods have advantages since the volume in which the root is known to be located can be steadily decreased. This method depends on the existence of a criterion for determining whether a root exists within a given volume. Here topological degree theory is exploited to provide this criterion. Only three-dimensional volumes are considered here. The result is of some use in locating roots and in illustrating the theory. The classification of roots as X-points or O-points and the generalization to three dimensions are also discussed. © 1992.