Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces

Authors:
Lin Zheng;Chuanqing Gu
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, China 200444;Department of Mathematics, Shanghai University, Shanghai, China 200444
Venue:
Numerical Algorithms
Year:
2012

Citing 6
Cited 0

Recurrence relations for rational cubic methods, part I. The Halley method

Computing
Recurrence relations for rational cubic methods II: the Chebyshev method

Computing
Avoiding the computation of the second Fre´chet-derivative in the convex acceleration of Newton's method

Journal of Computational and Applied Mathematics
Recurrence relations for a Newton-like method in Banach spaces

Journal of Computational and Applied Mathematics
Third-order iterative methods with applications to Hammerstein equations: A unified approach

Journal of Computational and Applied Mathematics
Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study the semilocal convergence for a fifth-order method for solving nonlinear equations in Banach spaces. The semilocal convergence of this method is established by using recurrence relations. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method. As compared with the Jarratt method in Hernández and Salanova (Southwest J Pure Appl Math 1:29---40, 1999) and the Multi-super-Halley method in Wang et al. (Numer Algorithms 56:497---516, 2011), the differentiability conditions of the convergence of the method in this paper are mild and the R-order is improved. Finally, we give some numerical applications to demonstrate our approach.