scholarly journals TENSOLVE: A Software Package for Solving Systems of Nonlinear Equations and Nonlinear Least Squares Problems Using Tensor Methods

1994 ◽  
Author(s):  
Ali Bouaricha ◽  
Robert B. Schnabel
Keyword(s):  
Least Squares ◽  
Nonlinear Equations ◽  
Software Package ◽  
Nonlinear Least Squares ◽  
Systems Of Nonlinear Equations ◽  
Least Squares Problems ◽  
Tensor Methods

scholarly journals A variant of the Levenberg-Marquardt method with adaptive parameters for systems of nonlinear equations

2021 ◽  
Vol 7 (1) ◽  
pp. 1241-1256
Author(s):  
Lin Zheng ◽  
◽  
Liang Chen ◽  
Yanfang Ma ◽  
◽  
...  
Keyword(s):  
Least Squares ◽  
Error Bound ◽  
Nonlinear Equations ◽  
Quadratic Convergence ◽  
Nonlinear Least Squares ◽  
Systems Of Nonlinear Equations ◽  
Local Error ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Wolfe Line Search

<abstract><p>The Levenberg-Marquardt method is one of the most important methods for solving systems of nonlinear equations and nonlinear least-squares problems. It enjoys a quadratic convergence rate under the local error bound condition. Recently, to solve nonzero-residue nonlinear least-squares problem, Behling et al. propose a modified Levenberg-Marquardt method with at least superlinearly convergence under a new error bound condtion <sup>[<xref ref-type="bibr" rid="b3">3</xref>]</sup>. To extend their results for systems of nonlinear equations, by choosing the LM parameters adaptively, we propose an efficient variant of the Levenberg-Marquardt method and prove its quadratic convergence under the new error bound condition. We also investigate its global convergence by using the Wolfe line search. The effectiveness of the new method is validated by some numerical experiments.</p></abstract>

scholarly journals Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems

Heliyon ◽  
2021 ◽  
pp. e07499
Author(s):  
Mahmoud Muhammad Yahaya ◽  
Poom Kumam ◽  
Aliyu Muhammed Awwal ◽  
Sani Aji
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Least Squares Problems ◽  
Gradient Algorithms

scholarly journals Gauss–Newton–Secant Method for Solving Nonlinear Least Squares Problems under Generalized Lipschitz Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 158
Author(s):  
Ioannis K. Argyros ◽  
Stepan Shakhno ◽  
Roman Iakymchuk ◽  
Halyna Yarmola ◽  
Michael I. Argyros
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Local Convergence ◽  
Nonlinear Least Squares ◽  
Computational Effort ◽  
Least Squares Problems ◽  
Restricted Region ◽  
Convergence Orders ◽  
Operator Decomposition ◽  
Lipschitz Conditions

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.

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