A convergence ball for multistep simplified newton-like methods

Xiaojun Chen, Tetsuro Yamamoto

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)15-24
Number of pages10
JournalNumerical Functional Analysis and Optimization
Issue number1-2
Publication statusPublished - 1 Jan 1993
Externally publishedYes


  • 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


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