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

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 derivativ...

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Published inMathematics (Basel) Vol. 7; no. 1; p. 99
Main Authors Argyros, Ioannis, Shakhno, Stepan, Shunkin, Yurii
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2019
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ISSN2227-7390
2227-7390
DOI10.3390/math7010099

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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.
AbstractList 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.
Author Argyros, Ioannis
Shakhno, Stepan
Shunkin, Yurii
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CitedBy_id crossref_primary_10_1016_j_ifacol_2020_12_1630
crossref_primary_10_1515_gmj_2023_2043
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Cites_doi 10.1007/s10958-014-1971-3
10.1137/1.9781611971200
10.1016/j.amc.2003.12.025
10.1007/s11075-011-9470-9
10.1016/j.amc.2010.09.040
10.1201/9781315153469
10.1080/01630568708816254
10.1016/j.amc.2013.09.049
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Copyright 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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StartPage 99
SubjectTerms Approximation
Convergence
differential-difference method
divided differences
Hypotheses
Iterative methods
Least squares
Mathematics
Methods
Nonlinear equations
nonlinear least squares problem
Operators (mathematics)
order of convergence
Parameter estimation
residual
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