Gauss–Newton–Secant Method for Solving Nonlinear Least Squares Problems under Generalized Lipschitz Conditions - Sorbonne Université
Article Dans Une Revue Axioms Année : 2021

Gauss–Newton–Secant Method for Solving Nonlinear Least Squares Problems under Generalized Lipschitz Conditions

Ioannis K Argyros
  • Fonction : Auteur
  • PersonId : 1112718
Stepan Shakhno
  • Fonction : Auteur
  • PersonId : 1028288
Halyna Yarmola
  • Fonction : Auteur
  • PersonId : 1028289
Michael I Argyros
  • Fonction : Auteur
  • PersonId : 1112719

Résumé

We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. We consider the case of both zero and nonzero residuals and determine their convergence orders. We use two types of Lipschitz conditions (center and restricted region conditions) to study the convergence of the method. Moreover, we obtain a larger radius of convergence and tighter error estimates than in previous works. Hence, we extend the applicability of this method under the same computational effort.
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Dates et versions

hal-03371094 , version 1 (08-10-2021)

Identifiants

Citer

Ioannis K Argyros, Stepan Shakhno, Roman Iakymchuk, Halyna Yarmola, Michael I Argyros. Gauss–Newton–Secant Method for Solving Nonlinear Least Squares Problems under Generalized Lipschitz Conditions. Axioms, 2021, 10 (3), pp.158. ⟨10.3390/axioms10030158⟩. ⟨hal-03371094⟩
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