Semilocal convergence of a sixth-order Jarratt method in Banach spaces

2010 ◽  
Vol 57 (4) ◽  
pp. 441-456 ◽  
Author(s):  
Xiuhua Wang ◽  
Jisheng Kou ◽  
Chuanqing Gu
Keyword(s):  
Banach Spaces ◽  
Semilocal Convergence ◽  
Sixth Order ◽  
Jarratt Method

On a sixth-order Jarratt-type method in Banach spaces

2015 ◽  
Vol 08 (04) ◽  
pp. 1550065 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Spaces ◽  
Semilocal Convergence ◽  
Fréchet Derivative ◽  
Sixth Order ◽  
Convergence Conditions ◽  
Type Method ◽  
Frechet Derivative ◽  
The Third ◽  
Local Convergence Analysis ◽  
Jarratt Method

We present a local convergence analysis of a sixth-order Jarratt-type method in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies such as [X. Wang, J. Kou and C. Gu, Semilocal convergence of a sixth-order Jarratt method in Banach spaces, Numer. Algorithms 57 (2011) 441–456.] require hypotheses up to the third Fréchet-derivative. Numerical examples are also provided in this study.

Semilocal convergence of a sixth-order method in Banach spaces

2012 ◽  
Vol 61 (3) ◽  
pp. 413-427 ◽  
Author(s):  
Lin Zheng ◽  
Chuanqing Gu
Keyword(s):  
Banach Spaces ◽  
Semilocal Convergence ◽  
Sixth Order ◽  
Order Method

A variant of Jarratt method with sixth-order convergence

2008 ◽  
Vol 204 (1) ◽  
pp. 14-19 ◽  
Author(s):  
Xiuhua Wang ◽  
Jisheng Kou ◽  
Yitian Li
Keyword(s):  
Sixth Order ◽  
Order Convergence ◽  
Jarratt Method

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

Deformed super-Halley’s iteration in Banach spaces and its local and semilocal convergence

2019 ◽  
Vol 30 (3-4) ◽  
pp. 413-431
Author(s):  
M. Prashanth ◽  
Abhimanyu Kumar ◽  
D. K. Gupta ◽  
S. S. Mosta
Keyword(s):  
Banach Spaces ◽  
Semilocal Convergence

Semilocal convergence of a sixth order iterative method for quadratic equations

2012 ◽  
Vol 62 (7) ◽  
pp. 833-841 ◽  
Author(s):  
S. Amat ◽  
M.A. Hernández ◽  
N. Romero
Keyword(s):  
Iterative Method ◽  
Semilocal Convergence ◽  
Sixth Order ◽  
Quadratic Equations

scholarly journals On the Semilocal Convergence of the Multi–Point Variant of Jarratt Method: Unbounded Third Derivative Case

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 540 ◽  
Author(s):  
Zhang Yong ◽  
Neha Gupta ◽  
J. P. Jaiswal ◽  
Kalyanasundaram Madhu
Keyword(s):  
Nonlinear Operator ◽  
A Priori ◽  
Semilocal Convergence ◽  
Continuity Condition ◽  
Fréchet Derivative ◽  
Third Order ◽  
Frechet Derivative ◽  
Initial Iterate ◽  
Jarratt Method ◽  
Third Derivative

In this paper, we study the semilocal convergence of the multi-point variant of Jarratt method under two different mild situations. The first one is the assumption that just a second-order Fréchet derivative is bounded instead of third-order. In addition, in the next one, the bound of the norm of the third order Fréchet derivative is assumed at initial iterate rather than supposing it on the domain of the nonlinear operator and it also satisfies the local ω -continuity condition in order to prove the convergence, existence-uniqueness followed by a priori error bound. During the study, it is noted that some norms and functions have to recalculate and its significance can be also seen in the numerical section.

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