Christopher Martin, Victoria Rayskin
An improved bisection method in two dimensions
(874K, pdf)

ABSTRACT.  An algorithm and supporting analysis are presented here for finding roots of systems of continuous equations in two dimensions by bisection iteration. In each iteration, an initial domain in R^2 is split into equally sized sub-domains. Investigating a candidate domain's bounding path for encirclements of the origin provides the test for containment of a solution, and the domains not guaranteed to contain a solution are discarded. Attention is paid to the potential for accidental convergence to a false solution, and sampling criteria for resolving the boundary are provided with particular emphasis on robust convergence.