Rate of convergence of the generalized newton algorithm using the fixed-point approach

R. Kalaba*, A. Tishler, J. S. Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper shows that the generalized Newton algorithm [GN(r)], developed by Kalaba and Tishler (Ref. 1), can be described as a fixed-point algorithm. In addition to specifying sufficient conditions for convergence of the GN(r), we show that, for r=1, 2, 3, its rate of convergence increases with the order of the derivatives which are used.

Original languageEnglish
Pages (from-to)543-555
Number of pages13
JournalJournal of Optimization Theory and Applications
Volume43
Issue number4
DOIs
StatePublished - Aug 1984

Keywords

  • Generalized Newton algorithm
  • fixed-point algorithm
  • higher-order derivatives
  • rate of convergence

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