The local and semilocal convergence analysis of new Newton-like iteration methods


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KARAKAYA V. , Dogan K., Atalan Y., BOUZARA N. E. H.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.3, pp.735-751, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1505-16
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.735-751
  • Keywords: Modified Newton algorithm, Picard S hybrid iteration, semilocal convergence, local convergence

Abstract

The aim of this paper is to find new iterative Newton-like schemes inspired by the modified Newton iterative algorithm and prove that these iterations are faster than the existing ones in the literature. We further investigate their behavior and finally illustrate the results by numerical examples.