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

Ioannis Argyros, Stepan Shakhno and Yurii Shunkin
Additional contact information
Ioannis Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Stepan Shakhno: Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine
Yurii Shunkin: Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine

Mathematics, 2019, vol. 7, issue 1, 1-13

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.

Keywords: nonlinear least squares problem; differential-difference method; divided differences; order of convergence; residual (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/1/99/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/1/99/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:1:p:99-:d:198927

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().