<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We present a local convergence analysis of inexact Gauss-Newton-like method (IGNLM) for solving nonlinear least-squares problems in a Euclidean space setting. The convergence analysis is based on our new idea of restricted convergence domains. Using this idea, we obtain a more precise information on the location of the iterates than in earlier studies leading to smaller majorizing functions. This way, our approach has the following advantages and under the same computational cost as in earlier studies: A large radius of convergence and more precise estimates on the distances involved to obtain a desired error tolerance. That is, we have a larger choice of initial points and fewer iterations are also needed to achieve the error tolerance. Special cases and numerical examples are also presented to show these advantages.</p></abstract>

We present a local convergence analysis of inexact Gauss-Newton-like method (IGNLM) for solving nonlinear least-squares problems in a Euclidean space setting. The convergence analysis is based on our new idea of restricted convergence domains. Using this idea, we obtain a more precise information on the location of the iterates than in earlier studies leading to smaller majorizing functions. This way, our approach has the following advantages and under the same computational cost as in earlier studies: A large radius of convergence and more precise estimates on the distances involved to obtain a desired error tolerance. That is, we have a larger choice of initial points and fewer iterations are also needed to achieve the error tolerance. Special cases and numerical examples are also presented to show these advantages.

Extended Local Analysis of Inexact Gauss-Newton-like Method for Least Square Problems using Restricted Convergence Domains

Department of Mathematical Sciences, Cameron University, Lawton, OK 73505,

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We present a local convergence analysis of inexact Gauss-Newton-like method (IGNLM) for solving nonlinear least-squares problems in a Euclidean space setting....

Extended Local Analysis of Inexact Gauss-Newton-like Method for Least Square Problems using Restricted Convergence Domains

Published Online: Sep 24, 2016

Page range: 17 - 33

Received: Feb 16, 2016

Accepted: Jun 17, 2016

DOI: https://doi.org/10.1515/awutm-2016-0002

Keywords
Inexact Gauss-Newton-like method, Euclidean space, Nonlinear least squares problems, weak Lipschitz condition, weak and center-weak Lipschitz condition, local convergence, restricted convergence domains

© 2016 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Extended Local Analysis of Inexact Gauss-Newton-like Method for Least Square Problems using Restricted Convergence Domains

Published Online: Sep 24, 2016

Page range: 17 - 33

Received: Feb 16, 2016

Accepted: Jun 17, 2016

DOI: https://doi.org/10.1515/awutm-2016-0002

KeywordsInexact Gauss-Newton-like method, Euclidean space, Nonlinear least squares problems, weak Lipschitz condition, weak and center-weak Lipschitz condition, local convergence, restricted convergence domains

© 2016 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Inexact Gauss-Newton-like method, Euclidean space, Nonlinear least squares problems, weak Lipschitz condition, weak and center-weak Lipschitz condition, local convergence, restricted convergence domains