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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Bibliographic Details
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
Subjects
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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ISSN2227-7390
2227-7390
DOI10.3390/math7010099

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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math7010099