scholarly journals Metaheuristic algorithm approach to solve non-linear equations system with complex roots

2020 ◽  
Vol 1494 ◽  
pp. 012001
Author(s):  
A Kamsyakawuni ◽  
M P Sari ◽  
A Riski ◽  
K A Santoso
Keyword(s):  
Linear Equations ◽  
Metaheuristic Algorithm ◽  
Complex Roots ◽  
Non Linear ◽  
Non Linear Equations

scholarly journals PENERAPAN COCKROACH SWARM OPTIMIZATION ALGORITHM (CSOA) PADA PENYELESAIAN PERSAMAAN POLINOMIAL YANG MEMILIKI AKAR KOMPLEKS

2018 ◽  
Vol 18 (2) ◽  
pp. 81
Author(s):  
Ema Fahma Farikha ◽  
Rusli Hidayat ◽  
Muhammad Ziaul Arif
Keyword(s):  
Optimization Algorithm ◽  
Linear Equations ◽  
Food Sources ◽  
Polynomial Equations ◽  
Metaheuristic Algorithm ◽  
Swarm Optimization ◽  
Non Linear Equation ◽  
Complex Roots ◽  
Non Linear ◽  
Newton Raphson

In this paper, we use a metaheuristic algorithm for solving non-linear equations (polynomial equations) which have a set of complex roots (complex numbers). The metaheuristic algorithm is the Cockroach Swarm Optimization Algorithm (CSOA) which imitate various types of natural cockroach behaviors such as chase-swarming, dispersing and ruthlessness when hunting for food sources. In this study, several examples of non-linear polynomial equations were used for evaluating the accuracy of CSOA. In this simulation, the accuracy comparison has been accomplished. It is shown that CSOA results are more accurate compared to the Newton-Raphson results. Keywords: Cockroach Swarm Optimization Algorithm, Complex roots of polynomial, Newton-Raphson, Non-Linear equation.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

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