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

Authors:
Xiaojian Zhou;Xin Chen;Yongzhong Song
Affiliations:
Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, People's Republic of China 210023 and School of Science, Nantong U ...;Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, People's Republic of China 210023;Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, People's Republic of China 210023
Venue:
Numerical Algorithms
Year:
2014

Citing 10
Cited 0

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)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
High-order nonlinear solver for multiple roots

Computers & Mathematics with Applications
New families of nonlinear third-order solvers for finding multiple roots

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

Journal of Computational and Applied Mathematics
Some fourth-order nonlinear solvers with closed formulae for multiple roots

Computers & Mathematics with Applications
Extension of Murakami's high-order non-linear solver to multiple roots

International Journal of Computer Mathematics
Constructing higher-order methods for obtaining the multiple roots of nonlinear equations

Journal of Computational and Applied Mathematics
Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center---Hölder continuous. Different from the technique and the hypothesis used by them, in this paper, we also investigate the convergence radius of the modified Newton method under the condition that the derivative $f^{(m)}$ of function f satisfies the center---Hölder continuous condition. The radius given here is larger than that given by Ren and Argyros. The uniqueness ball of solution is also discussed. Some examples are given to show applications of our theorem.