Nonstationary vs. stationary iterative processes

Luba Sapir, Tamara Kogan, Ariel Sapir, Amir Sapir

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we define s-nonstationary iterative process and obtain its properties. We prove, that for any one-point iterative process without memory, there exists an s-nonstationary process of the same order, but of higher efficiency by the criteria of Traub and Ostrowski. We supply constructions of s-nonstationary processes for Newton’s, Halley’s, and Chebyshev’s methods, obtain their properties and, for some of them, also their geometric interpretation. The algorithms we present can be transformed into computer programs in a straightforward manner. Additionally, we illustrate numerical examples, as demonstrations for the methods we present.

Original languageEnglish
Pages (from-to)515-535
Number of pages21
JournalNumerical Algorithms
Volume86
Issue number2
DOIs
StatePublished - 1 Feb 2021

Keywords

  • Index of informational efficiency
  • Iterative method
  • Kung–Traub conjecture
  • Order of convergence
  • Traub–Ostrowski index of computational efficiency

ASJC Scopus subject areas

  • Applied Mathematics

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