To the question of efficiency of iterative methods

Tamara Kogan, Luba Sapir, Amir Sapir, Ariel Sapir

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this paper we prove that, among all one-point iterative processes without memory of order p, the most efficient processes are of order p=3. Moreover, the computational efficiency of one-point iterative processes without memory decreases to 1 as p increases, i.e., the efficiency index of higher order of convergence methods is low. We find the upper and lower bounds of the Ostrowski–Traub index of computational efficiency in a wider class of iterative methods with unit informational efficiency.

Original languageEnglish
Pages (from-to)40-46
Number of pages7
JournalApplied Mathematics Letters
Volume66
DOIs
StatePublished - 1 Apr 2017

Keywords

  • Computational efficiency
  • Efficiency index
  • Informational efficiency
  • Iterative methods
  • One-point method without memory
  • Order of convergence

ASJC Scopus subject areas

  • Applied Mathematics

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