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Mathematics 2019, 7(1), 99; https://doi.org/10.3390/math7010099

Improved Convergence Analysis of Gauss-Newton-Secant Method for Solving Nonlinear Least Squares Problems

1
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
2
Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine
*
Author to whom correspondence should be addressed.
Received: 20 October 2018 / Revised: 12 January 2019 / Accepted: 15 January 2019 / Published: 18 January 2019
(This article belongs to the Special Issue Computational Methods in Analysis and Applications)
Full-Text   |   PDF [268 KB, uploaded 18 January 2019]

Abstract

We study an iterative differential-difference method for solving nonlinear least squares problems, which uses, instead of the Jacobian, the sum of derivative of differentiable parts of operator and divided difference of nondifferentiable parts. Moreover, we introduce a method that uses the derivative of differentiable parts instead of the Jacobian. Results that establish the conditions of convergence, radius and the convergence order of the proposed methods in earlier work are presented. The numerical examples illustrate the theoretical results. View Full-Text
Keywords: nonlinear least squares problem; differential-difference method; divided differences; order of convergence; residual nonlinear least squares problem; differential-difference method; divided differences; order of convergence; residual
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Argyros, I.; Shakhno, S.; Shunkin, Y. Improved Convergence Analysis of Gauss-Newton-Secant Method for Solving Nonlinear Least Squares Problems. Mathematics 2019, 7, 99.

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