Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative

Authors:
Weihong Bi;Hongmin Ren;Qingbiao Wu
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China 310027;Department of Information and Electronics, Hangzhou Polytechnic, Hangzhou, People's Republic of China 311400;Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China 310027
Venue:
Numerical Algorithms
Year:
2011

Citing 13
Cited 1

On the method of tangent hyperbolas on Banach spaces

Journal of Computational and Applied Mathematics
Recurrence relations for rational cubic methods, part I. The Halley method

Computing
A note on the Halley method in Banach spaces

Applied Mathematics and Computation
An optimal multiple root-finding method of order three

Journal of Computational and Applied Mathematics
Convergence and Complexity of Newton Iteration for Operator Equations

Journal of the ACM (JACM)
Indices of convexity and concavity: application to Halley method

Applied Mathematics and Computation
Modified Newton's method with third-order convergence and multiple roots

Journal of Computational and Applied Mathematics
The convergence ball of the Secant method under Hölder continuous divided differences

Journal of Computational and Applied Mathematics
Convergence of the family of the deformed Euler-Halley iterations under the Hölder condition of the second derivative

Journal of Computational and Applied Mathematics
Halley's method for operators with unbounded second derivative

Applied Numerical Mathematics
High-order nonlinear solver for multiple roots

Computers & Mathematics with Applications
On Newton-type methods for multiple roots with cubic convergence

Journal of Computational and Applied Mathematics
The convergence ball of Wang's method for finding a zero of a derivative

Mathematical and Computer Modelling: An International Journal

On the convergence radius of the modified Newton method for multiple roots under the center---Hölder condition

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, the estimate of the radius of the convergence ball of the modified Halley's method for finding multiple zeros of nonlinear equations is provided under the hypotheses that the derivative f (m驴+驴1) of function f is Hölder continuous, and f (m驴+驴1) is bounded. The uniqueness ball of solution is also established. Finally, some examples are provided to show applications of our theorem.