Semilocal convergence analysis and comparison of revisited computational efficiency of the sixth-order method in Banach spaces

2019 ◽  
Vol 49 (2) ◽  
pp. 1-16
Author(s):  
Jai Prakash Jaiswal
Keyword(s):  
Convergence Analysis ◽  
Banach Spaces ◽  
Computational Efficiency ◽  
Semilocal Convergence ◽  
Sixth Order ◽  
Order Method

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

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.

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