Are orthogonal transformations worthwhile for least squares problems?

1987 ◽  
Vol 22 (1) ◽  
pp. 14-19 ◽  
Author(s):  
Richard L Branham
Keyword(s):  
Least Squares ◽  
Least Squares Problems

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 Adaptive Robust Kernels for Non-Linear Least Squares Problems

2021 ◽  
pp. 1-1
Author(s):  
Nived Chebrolu ◽  
Thomas Labe ◽  
Olga Vysotska ◽  
Jens Behley ◽  
Cyrill Stachniss
Keyword(s):  
Least Squares ◽  
Linear Least Squares ◽  
Least Squares Problems ◽  
Non Linear ◽  
Linear Least Squares Problems

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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