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  4. Local convergence analysis of the Gauss-Newton-Kurchatov method

Local convergence analysis of the Gauss-Newton-Kurchatov method

MMC.
2020;
Volume 7, Number 2
: pp. 248–258
https://doi.org/10.23939/mmc2020.02.248
Received: March 18, 2020
Accepted: June 21, 2020

Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 248–258 (2020)

Authors:
  1. I. K. Argyros
  2. S. M. Shakhno
  3. H. P. Yarmola
1
Cameron University
2
Ivan Franko National University of Lviv
3
Ivan Franko National University of Lviv

We present a local convergence analysis of the Gauss-Newton-Kurchatov method  for solving nonlinear least squares problems with the decomposition of the operator.  The method uses the sum of the derivative of the differentiable part of the operator and the divided difference of the nondifferentiable part instead of computing  the full Jacobian.  A theorem, which establishes the conditions of convergence, radius, and the convergence order of the proposed method, is proved [1].  However, the radius of convergence is small in general limiting the choice of initial points.  Using tighter estimates on the distances, under weaker hypotheses [1], we provide an analysis of the Gauss--Newton--Kurchatov method with the following advantages over the corresponding results [1]: extended convergence region; finer error distances, and an at least as precise information on the location of the solution. The numerical examples illustrate the theoretical results.

Gauss-Newton-Kurchatov method
local convergence
Frechet-derivative
Lipschitz condition
Ccenter-Lipschitz condition
convergence domain
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