On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms

Xiaojun Chen

doi:10.1007/BF00050844

On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms

Xiaojun Chen

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

28 Citations (Scopus)

Abstract

In this paper, the author studies a Broyden-like method for solving nonlinear equations with nondifferentiable terms, which uses as updating matrices, approximations for Jacobian matrices of differentiable terms. Local and semilocal convergence theorems are proved. The results generalize those of Broyden, Dennis and Moré.

Original language	English
Pages (from-to)	387-401
Number of pages	15
Journal	Annals of the Institute of Statistical Mathematics
Volume	42
Issue number	2
DOIs	https://doi.org/10.1007/BF00050844
Publication status	Published - 1 Jun 1990
Externally published	Yes

Keywords

Broyden-like methods
Convergence theorems
nondifferentiable terms
nonlinear equations

ASJC Scopus subject areas

Statistics and Probability

More information

10.1007/BF00050844

Cite this

@article{b59f55632828472bbb936470eddabf04,

title = "On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms",

abstract = "In this paper, the author studies a Broyden-like method for solving nonlinear equations with nondifferentiable terms, which uses as updating matrices, approximations for Jacobian matrices of differentiable terms. Local and semilocal convergence theorems are proved. The results generalize those of Broyden, Dennis and Mor{\'e}.",

keywords = "Broyden-like methods, Convergence theorems, nondifferentiable terms, nonlinear equations",

author = "Xiaojun Chen",

year = "1990",

month = jun,

day = "1",

doi = "10.1007/BF00050844",

language = "English",

volume = "42",

pages = "387--401",

journal = "Annals of the Institute of Statistical Mathematics",

issn = "0020-3157",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms

AU - Chen, Xiaojun

PY - 1990/6/1

Y1 - 1990/6/1

N2 - In this paper, the author studies a Broyden-like method for solving nonlinear equations with nondifferentiable terms, which uses as updating matrices, approximations for Jacobian matrices of differentiable terms. Local and semilocal convergence theorems are proved. The results generalize those of Broyden, Dennis and Moré.

AB - In this paper, the author studies a Broyden-like method for solving nonlinear equations with nondifferentiable terms, which uses as updating matrices, approximations for Jacobian matrices of differentiable terms. Local and semilocal convergence theorems are proved. The results generalize those of Broyden, Dennis and Moré.

KW - Broyden-like methods

KW - Convergence theorems

KW - nondifferentiable terms

KW - nonlinear equations

UR - http://www.scopus.com/inward/record.url?scp=0000436840&partnerID=8YFLogxK

U2 - 10.1007/BF00050844

DO - 10.1007/BF00050844

M3 - Journal article

SN - 0020-3157

VL - 42

SP - 387

EP - 401

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 2

ER -

On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this