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.
Highlights
We aim to investigate the performance of a repulsion algorithm that is based on a penalty function and the Nelder-Mead (N-M) [1] local search procedure to compute multiple roots of a system of nonlinear equations of the form f ðxÞ 1⁄4 0; ð1Þ
The goal of these parameters is to adjust the penalty for already located minimizers. They may be used to reduce the radius of the repulsion area or to highly penalize the proximity to located solutions. We further explore this penalty-type approach to create repulsion areas around previously detected roots and propose a repulsion algorithm that is capable of computing multiple roots of a system of nonlinear equations invoking the N-M local procedure with modified merit functions
A repulsion algorithm is presented for locating multiple roots of a system of nonlinear equations
Summary
We further explore this penalty-type approach to create repulsion areas around previously detected roots and propose a repulsion algorithm that is capable of computing multiple roots of a system of nonlinear equations invoking the N-M local procedure with modified merit functions. Repulsion Algorithm doi:10.1371/journal.pone.0121844.t001 computing a minimizer of the merit function, given a sampled point y, is the N-M local procedure. This is the subject of the section. If simplex has collapsed ‘break’ or generate vertices using (11) with probability 0.75
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
