scholarly journals A unifying local–semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

2004 ◽  
Vol 298 (2) ◽  
pp. 374-397 ◽  
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Semilocal Convergence

Improved semilocal convergence analysis in Banach space with applications to chemistry

2017 ◽  
Vol 56 (7) ◽  
pp. 1958-1975 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Elena Giménez ◽  
Á. A. Magreñán ◽  
Í. Sarría ◽  
Juan Antonio Sicilia
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Semilocal Convergence

scholarly journals Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yueqing Zhao ◽  
Rongfei Lin ◽  
Zdenek Šmarda ◽  
Yasir Khan ◽  
Jinbiao Chen ◽  
...  
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Convergence Analysis ◽  
Operator Equation ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Semilocal Convergence ◽  
Nonlinear Operator Equation ◽  
Jarratt Method ◽  
Semilocal Convergence Theorem

Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem.

A convergence of a Steffensen-like method for solving nonlinear equations in a Banach space

2017 ◽  
Vol 26 (2) ◽  
pp. 125-136
Author(s):  
IOANNIS K. ARGYROS ◽  
SANTHOSH GEORGE
Keyword(s):  
Banach Space ◽  
Nonlinear Equation ◽  
Convergence Analysis ◽  
Unique Solution ◽  
Nonlinear Equations ◽  
Semilocal Convergence ◽  
Convergence Conditions ◽  
Numerical Example ◽  
Space Setting

We present a local as well as a semilocal convergence analysis of a Steffensen-like method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. This method generalizes and improves the sufficient convergence conditions of earlier methods. In particular, a numerical example is presented to show the advantages of our approach.

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 On a new semilocal convergence analysis for the Jarratt method

2013 ◽  
Vol 2013 (1) ◽  
pp. 194 ◽  
Author(s):  
Ioannis K Argyros ◽  
Yeol Cho ◽  
Sanjay Khattri
Keyword(s):  
Convergence Analysis ◽  
Semilocal Convergence ◽  
Jarratt Method

ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450007
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Lipschitz Condition ◽  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Model ◽  
Semilocal Convergence ◽  
Convergence Result ◽  
Numer Anal ◽  
The One

We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] in combination with the weaker center 2-piece L1-average Lipschitz condition given by us in this paper, we provide a tighter convergence analysis than the one given in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] which in turn has improved the works in earlier studies such as [R. L. Adler, J. P. Dedieu, J. Y. Margulies, M. Martens and M. Shub, Newton's method on Riemannian manifolds and a geometric model for the human spine, IMA J. Numer. Anal.22 (2002) 359–390; F. Alvarez, J. Bolte and J. Munier, A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math.8 (2008) 197–226; J. P. Dedieu, P. Priouret and G. Malajovich, Newton's method on Riemannian manifolds: Covariant α-theory, IMA J. Numer. Anal.23 (2003) 395–419].

scholarly journals Strong convergence analysis of a monotone projection algorithm in a Banach space

2016 ◽  
Vol 09 (05) ◽  
pp. 2865-2874 ◽  
Author(s):  
Xiaolong Qin ◽  
B. A. Bin Dehaish ◽  
Abdul Latif ◽  
Sun Young Cho
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Projection Algorithm
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