16-19 Christopher Martin, Victoria Rayskin

An improved bisection method in two dimensions (874K, pdf) Feb 18, 16

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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.

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