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Efficiency of the Multisection Method

03/06/2023

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by J. S. C. Prentice, et al.

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We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort algorithm that uses more sections than the bisection method, although this optimal algorithm is problem dependent. The number of sections required for optimality is determined by means of a Lambert W function.

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