Convergence domains of certain iterative methods for solving nonlinear equations

Xiaojun Chen; Tetsuro Yamamoto

doi:10.1080/01630568908816289

Convergence domains of certain iterative methods for solving nonlinear equations

Xiaojun Chen, Tetsuro Yamamoto

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

103 Citations (Scopus)

Abstract

In this paper, we consider the iterationxn+l=xn”A(xn)1(f(xn)+g(xn))• n=0,l,2. for solving the equation f(x)+g(x)=0, where f and g are operators in Banach spaces, f is Frechet differentiable, and A(x) is an approximation for f’(x), while the differentiability of g is not assumed. Under Zabrejko-Nguen type hypotheses, we determine a domain 9 such that starting from any point of Q the method converges to a solution of the equation.

Original language	English
Pages (from-to)	37-48
Number of pages	12
Journal	Numerical Functional Analysis and Optimization
Volume	10
Issue number	1-2
DOIs	https://doi.org/10.1080/01630568908816289
Publication status	Published - 1 Jan 1989
Externally published	Yes

ASJC Scopus subject areas

Computer Science Applications
Signal Processing
Analysis
Control and Optimization
Applied Mathematics

More information

10.1080/01630568908816289

Cite this

@article{a15bcf9df597441a982d21d9e2fad5f1,

title = "Convergence domains of certain iterative methods for solving nonlinear equations",

abstract = "In this paper, we consider the iterationxn+l=xn”A(xn)1(f(xn)+g(xn))• n=0,l,2. for solving the equation f(x)+g(x)=0, where f and g are operators in Banach spaces, f is Frechet differentiable, and A(x) is an approximation for f{\textquoteright}(x), while the differentiability of g is not assumed. Under Zabrejko-Nguen type hypotheses, we determine a domain 9 such that starting from any point of Q the method converges to a solution of the equation.",

author = "Xiaojun Chen and Tetsuro Yamamoto",

year = "1989",

month = jan,

day = "1",

doi = "10.1080/01630568908816289",

language = "English",

volume = "10",

pages = "37--48",

journal = "Numerical Functional Analysis and Optimization",

issn = "0163-0563",

publisher = "Taylor and Francis Ltd.",

number = "1-2",

}

TY - JOUR

T1 - Convergence domains of certain iterative methods for solving nonlinear equations

AU - Chen, Xiaojun

AU - Yamamoto, Tetsuro

PY - 1989/1/1

Y1 - 1989/1/1

N2 - In this paper, we consider the iterationxn+l=xn”A(xn)1(f(xn)+g(xn))• n=0,l,2. for solving the equation f(x)+g(x)=0, where f and g are operators in Banach spaces, f is Frechet differentiable, and A(x) is an approximation for f’(x), while the differentiability of g is not assumed. Under Zabrejko-Nguen type hypotheses, we determine a domain 9 such that starting from any point of Q the method converges to a solution of the equation.

AB - In this paper, we consider the iterationxn+l=xn”A(xn)1(f(xn)+g(xn))• n=0,l,2. for solving the equation f(x)+g(x)=0, where f and g are operators in Banach spaces, f is Frechet differentiable, and A(x) is an approximation for f’(x), while the differentiability of g is not assumed. Under Zabrejko-Nguen type hypotheses, we determine a domain 9 such that starting from any point of Q the method converges to a solution of the equation.

UR - http://www.scopus.com/inward/record.url?scp=0024302091&partnerID=8YFLogxK

U2 - 10.1080/01630568908816289

DO - 10.1080/01630568908816289

M3 - Journal article

SN - 0163-0563

VL - 10

SP - 37

EP - 48

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 1-2

ER -

Convergence domains of certain iterative methods for solving nonlinear equations

Abstract

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this