On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators

Xiaojun Chen; T. Yamamoto

doi:10.1007/BF02238652

On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators

Xiaojun Chen, T. Yamamoto

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

26 Citations (Scopus)

Abstract

In this paper, we study the convergence of some quasi-Newton methods for solving nonlinear equation Ax+g(x)=0 in a domain D⊄Rn, where A is an n×n matrix and g is a nondifferentiable but Lipschitz continuous operator. By interval analysis, we give a new convergence theorem of the methods.

Original language	English
Pages (from-to)	87-94
Number of pages	8
Journal	Computing
Volume	49
Issue number	1
DOIs	https://doi.org/10.1007/BF02238652
Publication status	Published - 1 Mar 1992
Externally published	Yes

Keywords

AMS Subject Classifications: 65H10, 65G10
convergence theorems
nondifferentiable operator
Nonlinear equations
quasi-Newton method

ASJC Scopus subject areas

Theoretical Computer Science
Software
Numerical Analysis
Computer Science Applications
Computational Theory and Mathematics
Computational Mathematics

More information

10.1007/BF02238652

Cite this

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abstract = "In this paper, we study the convergence of some quasi-Newton methods for solving nonlinear equation Ax+g(x)=0 in a domain D⊄Rn, where A is an n×n matrix and g is a nondifferentiable but Lipschitz continuous operator. By interval analysis, we give a new convergence theorem of the methods.",

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AU - Yamamoto, T.

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N2 - In this paper, we study the convergence of some quasi-Newton methods for solving nonlinear equation Ax+g(x)=0 in a domain D⊄Rn, where A is an n×n matrix and g is a nondifferentiable but Lipschitz continuous operator. By interval analysis, we give a new convergence theorem of the methods.

AB - In this paper, we study the convergence of some quasi-Newton methods for solving nonlinear equation Ax+g(x)=0 in a domain D⊄Rn, where A is an n×n matrix and g is a nondifferentiable but Lipschitz continuous operator. By interval analysis, we give a new convergence theorem of the methods.

KW - AMS Subject Classifications: 65H10, 65G10

KW - convergence theorems

KW - nondifferentiable operator

KW - Nonlinear equations

KW - quasi-Newton method

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U2 - 10.1007/BF02238652

DO - 10.1007/BF02238652

M3 - Journal article

SN - 0010-485X

VL - 49

SP - 87

EP - 94

JO - Computing

JF - Computing

IS - 1

ER -

On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators

Abstract

Keywords

ASJC Scopus subject areas

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