A convergence ball for multistep simplified newton-like methods

Xiaojun Chen; Tetsuro Yamamoto

doi:10.1080/01630569308816505

A convergence ball for multistep simplified newton-like methods

Xiaojun Chen, Tetsuro Yamamoto

Research output: Journal article publication › Journal article › Academic research › peer-review

2 Citations (Scopus)

Abstract

We first give a local convergence ball for multistep simplified New-ton-like methods for solving nonlinear equations with nondifferentiable operators. Next we apply the results to some iterative methods and derive Rheinboldt’s ball for Newton's method. Rall's result for Newton’s method is also extenciec to the multistep simplified Newton method. Furthermore, we use Rall's example to see how the size of the convergence ball varies along with the multistep number.

Original language	English
Pages (from-to)	15-24
Number of pages	10
Journal	Numerical Functional Analysis and Optimization
Volume	14
Issue number	1-2
DOIs	https://doi.org/10.1080/01630569308816505
Publication status	Published - 1 Jan 1993
Externally published	Yes

Keywords

A convergence ball
methods
multistep simplified Newton-like
nonlinear equations with nondifferentiable operators

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

More information

10.1080/01630569308816505

Cite this

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AB - We first give a local convergence ball for multistep simplified New-ton-like methods for solving nonlinear equations with nondifferentiable operators. Next we apply the results to some iterative methods and derive Rheinboldt’s ball for Newton's method. Rall's result for Newton’s method is also extenciec to the multistep simplified Newton method. Furthermore, we use Rall's example to see how the size of the convergence ball varies along with the multistep number.

KW - A convergence ball

KW - methods

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KW - nonlinear equations with nondifferentiable operators

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A convergence ball for multistep simplified newton-like methods

Abstract

Keywords

ASJC Scopus subject areas

More information

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