On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations

2011 ◽  
Vol 151 (1) ◽  
pp. 163-174 ◽  
Author(s):  
J. A. Ezquerro ◽  
M. Grau-Sánchez ◽  
A. Grau ◽  
M. A. Hernández ◽  
M. Noguera ◽  
...  
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Accelerated Convergence

SOME HIGH ORDER ITERATIVE METHODS FOR NONLINEAR EQUATIONS BASED ON THE MODIFIED HOMOTOPY PERTURBATION METHODS

2010 ◽  
Vol 03 (03) ◽  
pp. 395-408
Author(s):  
Bilian Chen ◽  
Yajun Xie ◽  
Changfeng Ma
Keyword(s):  
Nonlinear Equation ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Perturbation Methods ◽  
Systems Of Nonlinear Equations ◽  
Convergence Criteria ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Nonlinear Equation Systems ◽  
High Order Iterative Methods

In this paper, we present some efficient iterative methods for solving nonlinear equation (systems of nonlinear equations, respectively) by using modified homotopy perturbation methods. We also discuss the convergence criteria of the present methods. Some numerical examples are given to illustrate the performance and efficiency of the proposed methods.

scholarly journals A Family of Iterative Methods for Solving Systems of Nonlinear Equations Having Unknown Multiplicity

Algorithms ◽  
2015 ◽  
Vol 9 (1) ◽  
pp. 5 ◽  
Author(s):  
Fayyaz Ahmad ◽  
S. Serra-Capizzano ◽  
Malik Ullah ◽  
A. Al-Fhaid
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations

Multi-Point Iterative Methods for Systems of Nonlinear Equations

2009 ◽  
pp. 259-267 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations

scholarly journals Constructing Frozen Jacobian Iterative Methods for Solving Systems of Nonlinear Equations, Associated with ODEs and PDEs Using the Homotopy Method

Algorithms ◽  
2016 ◽  
Vol 9 (1) ◽  
pp. 18 ◽  
Author(s):  
Uswah Qasim ◽  
Zulifqar Ali ◽  
Fayyaz Ahmad ◽  
Stefano Serra-Capizzano ◽  
Malik Zaka Ullah ◽  
...  
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Homotopy Method ◽  
Systems Of Nonlinear Equations

scholarly journals New Multi-Step Iterative Methods for Solving Systems of Nonlinear Equations and Their Application on GNSS Pseudorange Equations

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 5976
Author(s):  
Kalyanasundaram Madhu ◽  
Arul Elango ◽  
René Jr Landry ◽  
Mo’tassem Al-arydah
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Computation Time ◽  
Efficiency Index ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Additional Function ◽  
Computation Efficiency ◽  
Global Navigation Satellite

A two-step fifth and a multi-step 5+3r order iterative method are derived, r≥1 for finding the solution of system of nonlinear equations. The new two-step fifth order method requires two functions, two first order derivatives, and the multi-step methods needs a additional function per step. The performance of this method has been tested with finding solutions to several test problems then applied to solving pseudorange nonlinear equations on Global Navigation Satellite Signal (GNSS). To solve the problem, at least four satellite’s measurements are needed to locate the user position and receiver time offset. In this work, a number of satellites from 4 to 8 are considered such that the number of equations is more than the number of unknown variables to calculate the user position. Moreover, the Geometrical Dilution of Precision (GDOP) values are computed based on the satellite selection algorithm (fuzzy logic method) which could be able to bring the best suitable combination of satellites. We have restricted the number of satellites to 4 to 6 for solving the pseudorange equations to get better GDOP value even after increasing the number of satellites beyond six also yields a 0.4075 GDOP value. Actually, the conventional methods utilized in the position calculation module of the GNSS receiver typically converge with six iterations for finding the user position whereas the proposed method takes only three iterations which really decreases the computation time which provide quicker position calculation. A practical study was done to evaluate the computation efficiency index (CE) and efficiency index (IE) of the new model. From the simulation outcomes, it has been noted that the new method is more efficient and converges 33% faster than the conventional iterative methods with good accuracy of 92%.

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