Convergence domains of certain iterative methods for solving nonlinear equations

Xiaojun Chen, Tetsuro Yamamoto

Research output: Journal article publicationJournal articleAcademic researchpeer-review

94 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 languageEnglish
Pages (from-to)37-48
Number of pages12
JournalNumerical Functional Analysis and Optimization
Volume10
Issue number1-2
DOIs
Publication statusPublished - 1 Jan 1989
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science Applications
  • Signal Processing
  • Analysis
  • Control and Optimization
  • Applied Mathematics

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