Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

Gisela C V Ramadas, Ana Maria A C Rocha and Edite M G P Fernandes

PLOS ONE, 2015, vol. 10, issue 4, 1-30

Abstract: This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as ‘erf’, is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0121844

DOI: 10.1371/journal.pone.0121844

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