Finding all solutions of systems of nonlinear equations with free variables

2007 ◽  
Vol 39 (6) ◽  
pp. 649-659 ◽  
Author(s):  
J.-F. Tsai ◽  
M.-H. Lin
Keyword(s):  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Free Variables ◽  
All Solutions

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

2015 ◽  
Vol 19 (5) ◽  
pp. 697-707 ◽  
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.

Mapped continuation methods for computing all solutions to general systems of nonlinear equations

1990 ◽  
Vol 14 (1) ◽  
pp. 71-85 ◽  
Author(s):  
J.D. Seader ◽  
M. Kuno ◽  
W.-J. Lin ◽  
S.A. Johnson ◽  
K. Unsworth ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Continuation Methods ◽  
Systems Of Nonlinear Equations ◽  
All Solutions ◽  
General Systems

scholarly journals A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rami Sihwail ◽  
Obadah Said Solaiman ◽  
Khairuddin Omar ◽  
Khairul Akram Zainol Ariffin ◽  
Mohammed Alswaitti ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Hybrid Approach ◽  
Systems Of Nonlinear Equations
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