scholarly journals A new method for solving nonlinear systems of equations that is based on functional iterations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 605-630 ◽  
Author(s):  
Joaquín Moreno ◽  
Miguel A. López ◽  
Raquel Martínez
Keyword(s):  
Fixed Point ◽  
Nonlinear Systems ◽  
Linear Algebra ◽  
Linear Equations ◽  
Continuous Functions ◽  
Compact Set ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Banach Theorem ◽  
Non Linear Equations

Abstract Regarding solving nonlinear equations systems, there is a main problem that is the number and complexity of the linear algebra operations, and the functional evaluations of the applied algorithm. In this paper, an alternative solution will be proposed by means of constructing a converse of the Banach Theorem fixed-point, only to ℝ2 and ℝ3, in the following sense, this being: each root of a non-linear equations system has been considered as a fixed-point. Besides, the compact set and the continuous functions that fulfil the Banach Theorem are built under certain conditions, those that must satisfy the systemfunctions. Thus each iteration only requires the evaluation of two or three functions.

scholarly journals Solution of Nonlinear Systems of Equations via Metaheuristics

2019 ◽  
Vol 4 (5) ◽  
pp. 1108-1126
Author(s):  
Sangeeta Pant ◽  
Anuj Kumar ◽  
Mangey Ram
Keyword(s):  
Nonlinear Systems ◽  
Optimization Algorithm ◽  
Linear Equations ◽  
Optimization Technique ◽  
System Of Nonlinear Equations ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
New Techniques ◽  
Complex Nonlinear System ◽  
Non Linear Equations

A framework devoted to the solution of nonlinear systems of equations using grey wolf optimization algorithm (GWO) and a multi-objective particle swarm optimization algorithm (MOPSO) is presented in this work. Due to several numerical issues and very high computational complexity, it is hard to find the solution of such a complex nonlinear system of equations. It then explains that the problem of solution to a system of nonlinear equations can be simplified by viewing it as an optimization problem and solutions can be obtained by applying a nature inspired optimization technique. The results achieved are compared with classical as well as new techniques established in the literature. The proposed framework also seems to be very effective for the problems of system of non-linear equations arising in the various fields of science. For this purpose, the problem of neurophysiology application and the problem of combustion of hydrocarbons are considered for testing. Empirical results show that the presented framework is bright to deal with the high dimensional equations system.

scholarly journals Two elementary applications of some Presic type fixed point theorems

2011 ◽  
Vol 20 (1) ◽  
pp. 32-42
Author(s):  
VASILE BERINDE ◽  
◽  
MADALINA PACURAR ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Nonlinear Systems ◽  
Fixed Point Theorems ◽  
Fixed Point Method ◽  
Point Method ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Recurrence Sequences

We introduce and illustrate by suitable examples the use of a unified fixed point method for studying the convergence of nonlinear recurrence sequences and for solving cyclic nonlinear systems of equations. Our technique is essentially based on some Presic type fixed point theorems.

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