Study of semilocal convergence analysis of Chebyshev’s method under new type majorant conditions

SeMA Journal ◽  
2021 ◽  
Author(s):  
Chandni Kumari ◽  
P. K. Parida
Keyword(s):  
Convergence Analysis ◽  
Semilocal Convergence ◽  
Chebyshev’S Method ◽  
New Type

Convergence Analysis of the Modified Chebyshev’s Method for Finding Multiple Roots

2021 ◽  
Author(s):  
Rongfei Lin ◽  
Hongmin Ren ◽  
Qingbiao Wu ◽  
Yasir Khan ◽  
Juelian Hu
Keyword(s):  
Convergence Analysis ◽  
Multiple Roots ◽  
Chebyshev’S Method

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 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 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.

scholarly journals Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces

2018 ◽  
Vol 15 (06) ◽  
pp. 1850048
Author(s):  
Sukhjit Singh ◽  
Dharmendra Kumar Gupta ◽  
Randhir Singh ◽  
Mehakpreet Singh ◽  
Eulalia Martinez
Keyword(s):  
Convergence Analysis ◽  
Banach Spaces ◽  
Semilocal Convergence ◽  
Fréchet Derivative ◽  
Frechet Derivative ◽  
First Order ◽  
Weaker Conditions ◽  
Fifth Order ◽  
Derivatives Of ◽  
Text Condition

The convergence analysis both local under weaker Argyros-type conditions and semilocal under [Formula: see text]-condition is established using first order Fréchet derivative for an iteration of fifth order in Banach spaces. This avoids derivatives of higher orders which are either difficult to compute or do not exist at times. The Lipchitz and the Hölder conditions are particular cases of the [Formula: see text]-condition. Examples can be constructed for which the Lipchitz and Hölder conditions fail but the [Formula: see text]-condition holds. Recurrence relations are used for the semilocal convergence analysis. Existence and uniqueness theorems and the error bounds for the solution are provided. Different examples are solved and convergence balls for each of them are obtained. These examples include Hammerstein-type integrals to demonstrate the applicability of our approach.

Semilocal convergence analysis for the modified Newton-HSS method under the Hölder condition

2015 ◽  
Vol 72 (3) ◽  
pp. 667-685
Author(s):  
Minhong Chen ◽  
Qingbiao Wu ◽  
Rongfei Lin
Keyword(s):  
Convergence Analysis ◽  
Semilocal Convergence ◽  
Hölder Condition
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