Modified Secant-type methods for unconstrained optimization

Kahya E.

APPLIED MATHEMATICS AND COMPUTATION, cilt.181, sa.2, ss.1349-1356, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 181 Sayı: 2
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.amc.2006.03.003
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1349-1356
  • Anahtar Kelimeler: unconstrained optimization, univariate optimization, Newton method, Secant method, test functions, initial point, UNIDIMENSIONAL SEARCH METHOD
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

For solving nonlinear, univariate and unconstrained optimization problems, Newton method is an important and basic method which convergences quadratically. In this paper, we suggest a family of three new modifications of the classical Secant method where the iteration formula including an approximation of f'(x(k)) is satisfied by a recursive scheme. The efficiencies of the new methods are analyzed in terms of the most popular and widely used criterion; the number of iterations, in comparison with the Newton and Secant methods using six test functions. (c) 2006 Elsevier Inc. All rights reserved.