scholarly journals Design, Analysis, and Applications of Iterative Methods for Solving Nonlinear Systems

10.5772/64106 ◽  
2016 ◽  
Author(s):  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
Maria P. Vassileva
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Design Analysis

scholarly journals Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems

Algorithms ◽  
2016 ◽  
Vol 9 (1) ◽  
pp. 14 ◽  
Author(s):  
Xiaofeng Wang ◽  
Xiaodong Fan
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Derivative Free

On the improvement of the order of convergence of iterative methods for solving nonlinear systems by means of memory

2020 ◽  
Vol 104 ◽  
pp. 106277 ◽  
Author(s):  
Francisco I. Chicharro ◽  
Alicia Cordero ◽  
Neus Garrido ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Order Of Convergence

Third and fourth order iterative methods free from second derivative for nonlinear systems

2009 ◽  
Vol 211 (1) ◽  
pp. 190-197 ◽  
Author(s):  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Fourth Order ◽  
Second Derivative

A multi-step class of iterative methods for nonlinear systems

2013 ◽  
Vol 8 (3) ◽  
pp. 1001-1015 ◽  
Author(s):  
Fazlollah Soleymani ◽  
Taher Lotfi ◽  
Parisa Bakhtiari
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods

scholarly journals Some new efficient multipoint iterative methods for solving nonlinear systems of equations

2014 ◽  
Vol 92 (9) ◽  
pp. 1921-1934 ◽  
Author(s):  
Taher Lotfi ◽  
Parisa Bakhtiari ◽  
Alicia Cordero ◽  
Katayoun Mahdiani ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Multipoint Iterative Methods

scholarly journals Modified Dai-Yuan iterative scheme for Nonlinear Systems and its Application

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammed Yusuf Waziri ◽  
Kabiru Ahmed ◽  
Abubakar Sani Halilu ◽  
Aliyu Mohammed Awwal
Keyword(s):  
Nonlinear Systems ◽  
Global Convergence ◽  
Iterative Methods ◽  
Nonsmooth Optimization ◽  
Projection Method ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Search Direction ◽  
Derivative Free ◽  
Convergence Of The Scheme

<p style='text-indent:20px;'>By exploiting the idea employed in the spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and the approach applied in the modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a Dai-Yuan type iterative scheme for convex constrained nonlinear monotone system. The scheme's algorithm is obtained by combining its search direction with the projection method [Kluwer Academic Publishers, pp. 355-369(1998)]. One of the new scheme's attribute is that it is derivative-free, which makes it ideal for solving non-smooth problems. Furthermore, we demonstrate the method's application in image de-blurring problems by comparing its performance with a recent effective method. By employing mild assumptions, global convergence of the scheme is determined and results of some numerical experiments show the method to be favorable compared to some recent iterative methods.</p>

Estimation of the regions of attraction for autonomous nonlinear systems

2018 ◽  
Vol 41 (1) ◽  
pp. 97-106
Author(s):  
Guoqiang Yuan ◽  
Yinghui Li
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Jacobi Equation ◽  
Time Dependent ◽  
Implicit Function ◽  
Region Of Attraction ◽  
Sublevel Set ◽  
Initial Domain ◽  
Regions Of Attraction ◽  
Hamilton Jacobi Equation

A methodology for estimating the region of attraction for autonomous nonlinear systems is developed. The methodology is based on a proof that the region of attraction can be estimated accurately by the zero sublevel set of an implicit function which is the viscosity solution of a time-dependent Hamilton–Jacobi equation. The methodology starts with a given initial domain and yields a sequence of region of attraction estimates by tracking the evolution of the implicit function. The resulting sequence is contained in and converges to the exact region of attraction. While alternative iterative methods for estimating the region of attraction have been proposed, the methodology proposed in this paper can compute the region of attraction to achieve any desired accuracy in a dimensionally independent and efficient way. An implementation of the proposed methodology has been developed in the Matlab environment. The correctness and efficiency of the methodology are verified through a few examples.

scholarly journals Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems

2018 ◽  
Vol 323 ◽  
pp. 43-57 ◽  
Author(s):  
Abdolreza Amiri ◽  
Alicia Cordero ◽  
M. Taghi Darvishi ◽  
Juan R. Torregrosa
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Iterative Methods ◽  
Parametric Family ◽  
Seventh Order
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