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Gauss–Newton–Secant Method for Solving Nonlinear Least Squares Problems under Generalized Lipschitz Conditions
| Content Provider | MDPI |
|---|---|
| Author | Argyros, Ioannis Shakhno, Stepan Iakymchuk, Roman Yarmola, Halyna Argyros, Michael |
| Copyright Year | 2021 |
| Description | We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. We consider the case of both zero and nonzero residuals and determine their convergence orders. We use two types of Lipschitz conditions (center and restricted region conditions) to study the convergence of the method. Moreover, we obtain a larger radius of convergence and tighter error estimates than in previous works. Hence, we extend the applicability of this method under the same computational effort. |
| Starting Page | 158 |
| e-ISSN | 20751680 |
| DOI | 10.3390/axioms10030158 |
| Journal | Axioms |
| Issue Number | 3 |
| Volume Number | 10 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2021-07-21 |
| Access Restriction | Open |
| Subject Keyword | Axioms Mathematical Social Sciences Nonlinear Least Squares Problem Differential-difference Method Divided Differences Radius of Convergence Residual Error Estimates |
| Content Type | Text |
| Resource Type | Article |
