A performance comparison of the zero-finding by extended interval Newton method for Peano monosplines

Chen, Chin-Yun

doi:10.1016/j.amc.2012.12.008

Cited by 6 publications

(1 citation statement)

References 13 publications

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“…2) Homotopy Continuation (Embedding) Methods: In these methods, a hard problem is first transformed into a much simpler one, and then this simpler problem gradually deforms into the original one, e.g., [24] and [25]. 3) Interval-Newton Methods: The classical Newton-like iterative methods are applied to the interval variables in the interval-Newton methods, e.g., [26] and [27]. 4) Deterministic Branch-and-Bound Methods: These methods transform an NES into a global optimization problem, and then the transformed optimization problem is solved by the branch-and-bound methods, e.g., [20] and [28].…”

Section: A Related Workmentioning

confidence: 99%

Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution

Gong

Wang

Cai

et al. 2020

IEEE Trans. Syst. Man Cybern, Syst.

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Abstract-Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate.

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