A unified local convergence analysis of inexact constrained Levenberg–Marquardt methods

2011 ◽  
Vol 6 (5) ◽  
pp. 927-940 ◽  
Author(s):  
Roger Behling ◽  
Andreas Fischer
Keyword(s):  
Convergence Analysis ◽  
Local Convergence ◽  
Levenberg Marquardt ◽  
Local Convergence Analysis

scholarly journals Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 804
Author(s):  
Ioannis K. Argyros ◽  
Neha Gupta ◽  
J. P. Jaiswal
Keyword(s):  
Approximate Solution ◽  
Convergence Analysis ◽  
Banach Spaces ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Local Convergence ◽  
Existence And Uniqueness ◽  
Numerical Illustration ◽  
Type Method ◽  
Local Convergence Analysis

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

Semi-local convergence of a Newton-like method for solving equations with a singular derivative

2018 ◽  
Vol 27 (1) ◽  
pp. 01-08
Author(s):  
IOANNIS K. ARGYROS ◽  
◽  
GEORGE SANTHOSH ◽  
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Real Line ◽  
Local Convergence ◽  
Approximate Solutions ◽  
Convergence Domain ◽  
Solving Equations ◽  
Solutions Of Equations ◽  
Local Convergence Analysis ◽  
Special Case

We present a semi-local convergence analysis for a Newton-like method to approximate solutions of equations when the derivative is not necessarily non-singular in a Banach space setting. In the special case when the equation is defined on the real line the convergence domain is improved for this method when compared to earlier results. Numerical results where earlier results cannot apply but the new results can apply to solve nonlinear equations are also presented in this study.

scholarly journals Local Convergence Analysis of an Eighth Order Scheme Using Hypothesis Only on the First Derivative

Algorithms ◽  
2016 ◽  
Vol 9 (4) ◽  
pp. 65 ◽  
Author(s):  
Ioannis Argyros ◽  
Ramandeep Behl ◽  
Sandile Motsa
Keyword(s):  
Convergence Analysis ◽  
Local Convergence ◽  
Eighth Order ◽  
First Derivative ◽  
Order Scheme ◽  
Local Convergence Analysis

scholarly journals LOCAL CONVERGENCE ANALYSIS OF INEXACT NEWTON-LIKE METHODS

2009 ◽  
Vol 02 (01) ◽  
pp. 11-18 ◽  
Author(s):  
IOANNIS K. ARGYROS ◽  
SAID HILOUT
Keyword(s):  
Convergence Analysis ◽  
Local Convergence ◽  
Local Convergence Analysis

Improved local convergence analysis of the Gauss–Newton method under a majorant condition

2014 ◽  
Vol 60 (2) ◽  
pp. 423-439 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Á. Alberto Magreñán
Keyword(s):  
Convergence Analysis ◽  
Newton Method ◽  
Local Convergence ◽  
Majorant Condition ◽  
Local Convergence Analysis

New semilocal and local convergence analysis for the Secant method

2015 ◽  
Vol 262 ◽  
pp. 298-307 ◽  
Author(s):  
Á. Alberto Magreñán ◽  
Ioannis K. Argyros
Keyword(s):  
Convergence Analysis ◽  
Local Convergence ◽  
Secant Method ◽  
Local Convergence Analysis
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