A class of exponential quadratically convergent iterative formulae for unconstrained optimization

Kahya E.

APPLIED MATHEMATICS AND COMPUTATION, vol.186, no.2, pp.1010-1017, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 186 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1016/j.amc.2006.08.040
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1010-1017
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

For solving nonlinear, univariate and unconstrained optimization problems, Newton method is an important and basic method which converges quadratically. This paper presents a class of exponential iterative formulae. Convergence analyses show that the proposed methods converge quadratically. The efficiencies of the methods are analyzed in terms of the most popular and widely used criterion in comparison with the classical Newton method using five test functions. Numerical results indicate that one of the new exponential iterative formulae is effective and comparable to well-known Newton's method. (c) 2006 Elsevier Inc. All rights reserved.