A bisection method for systems of nonlinear equations
ACM Transactions on Mathematical Software (TOMS)
A methodology for solving chemical equilibrium systems
Applied Mathematics and Computation
Some tests of generalized bisection
ACM Transactions on Mathematical Software (TOMS)
Some tests of generalized bisection
ACM Transactions on Mathematical Software (TOMS)
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Lower bound functions for polynomials
Journal of Computational and Applied Mathematics
A linear relaxation technique for the position analysis of multiloop linkages
IEEE Transactions on Robotics
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Box-bisection is a method for solving nonlinear systems. Space is subdivided into boxes of smallerand smaller diameter, and each subbox is tested for the existence of solutions by a test that eithereliminates it from further consideration or marks it for subdivision. Simple bisection uses a test forthe exclusion of subboxes, but no test that guarantees the existence of a unique solution in a subbox.Using this simple bisection, we show that the passed boxes tend to cluster in geometrical configura-tions whose number is stable under subdivision. This implies for many problems that the workrequired to do simple bisection may be prohibitive. However, improvements may be possible bygrouping clusters and dynamically redefining the box proportions. The restriction to second-degreesystems is sufficient to display this behavior.