An efficient algorithm for finding all solutions of separable systems of nonlinear equations

In the tolerance analysis of electronic circuits, the concept of set-valued function is often useful. In this paper, an efficient algorithm is proposed for finding all solution sets of nonlinear resistive circuits described by systems of nonlinear equations containing set-valued functions termed piecewise-trapezoidal (PWT) functions. By numerical examples, the effectiveness of the proposed algorithm is confirmed from various viewpoints. It is also shown that the proposed algorithm could find all solution regions to a system of 1000 PWT equations in practical computation time.

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Modification of Species-Based Differential Evolution for Finding All Solutions of Systems of Nonlinear Equations

Proceedings of the Proceedings of The 5th Annual International Seminar on Trends in Science and Science Education, AISTSSE 2018, 18-19 October 2018, Medan, Indonesia ◽

10.4108/eai.18-10-2018.2287372 ◽

2019 ◽

Author(s):

Said Iskandar ◽

Didi Febrian ◽

Faridawaty Marpaung ◽

Ayu Adela

Keyword(s):

Differential Evolution ◽

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

All Solutions

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Finding All Solutions of Systems of Nonlinear Equations Using Spiral Dynamics Inspired Optimization with Clustering

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2015.p0697 ◽

2015 ◽

Vol 19 (5) ◽

pp. 697-707 ◽

Cited By ~ 5

Author(s):

Kuntjoro Adji Sidarto ◽

◽

Adhe Kania

Keyword(s):

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

System Of Nonlinear Equations ◽

Advantages And Disadvantages ◽

Root Finding ◽

Spiral Dynamics ◽

All Solutions ◽

Computational Sciences ◽

System Equations ◽

Novel Method

Nowadays the root finding problem for nonlinear system equations is still one of the difficult problems in computational sciences. Many attempts using deterministic and meta-heuristic methods have been done with their advantages and disadvantages, but many of them have fail to converge to all possible roots. In this paper, a novel method of locating and finding all of the real roots from the system of nonlinear equations is proposed mainly using the spiral dynamics inspired optimization by Tamura and Yasuda [1]. The method is improved by the usage of the Sobol sequence of points for generating initial candidates of roots which are uniformly distributed than of pseudo-random generated points. Using clustering technique, the method localizes all potential roots so the optimization is conducted in those points simultaneously. A set of problems as the benchmarks from the literature is given. Having only a single run for each problem, the proposed method has successfully found all possible roots within a bounded domain.

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