Next Article in Journal
High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions
Next Article in Special Issue
Two-Step Solver for Nonlinear Equations
Previous Article in Journal
Chiral Neuronal Motility: The Missing Link between Molecular Chirality and Brain Asymmetry
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Symmetry
Volume 11
Issue 1
10.3390/sym11010103
symmetry-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Local Convergence of a Family of Weighted-Newton Methods

by
Ramandeep Behl
1,*,
Ioannis K. Argyros
2,
J.A. Tenreiro Machado
3 and
Ali Saleh Alshomrani
1
1
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
3
Institute of Engineering, Polytechnic of Porto Department of Electrical Engineering, 4200-072 Porto, Portugal
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(1), 103; https://doi.org/10.3390/sym11010103
Submission received: 9 December 2018 / Revised: 11 January 2019 / Accepted: 12 January 2019 / Published: 17 January 2019
(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)
Versions Notes

Abstract

This article considers the fourth-order family of weighted-Newton methods. It provides the range of initial guesses that ensure the convergence. The analysis is given for Banach space-valued mappings, and the hypotheses involve the derivative of order one. The convergence radius, error estimations, and results on uniqueness also depend on this derivative. The scope of application of the method is extended, since no derivatives of higher order are required as in previous works. Finally, we demonstrate the applicability of the proposed method in real-life problems and discuss a case where previous studies cannot be adopted.
Keywords: Banach space; weighted-Newton method; local convergence; Fréchet-derivative; ball radius of convergence Banach space; weighted-Newton method; local convergence; Fréchet-derivative; ball radius of convergence

Share and Cite

MDPI and ACS Style

Behl, R.; K. Argyros, I.; Machado, J.A.T.; Alshomrani, A.S. Local Convergence of a Family of Weighted-Newton Methods. Symmetry 2019, 11, 103. https://doi.org/10.3390/sym11010103

AMA Style

Behl R, K. Argyros I, Machado JAT, Alshomrani AS. Local Convergence of a Family of Weighted-Newton Methods. Symmetry. 2019; 11(1):103. https://doi.org/10.3390/sym11010103

Chicago/Turabian Style

Behl, Ramandeep, Ioannis K. Argyros, J.A. Tenreiro Machado, and Ali Saleh Alshomrani. 2019. "Local Convergence of a Family of Weighted-Newton Methods" Symmetry 11, no. 1: 103. https://doi.org/10.3390/sym11010103

APA Style

Behl, R., K. Argyros, I., Machado, J. A. T., & Alshomrani, A. S. (2019). Local Convergence of a Family of Weighted-Newton Methods. Symmetry, 11(1), 103. https://doi.org/10.3390/sym11010103

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop