<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this report we show that the iterated regularization scheme due to Riley and Golub, sometimes also called the iterated Tikhonov regularization, can be generalized to damped least squares problems where the weights matrix <italic>D</italic> is not necessarily the identity but a general symmetric and positive definite matrix. We show that the iterative scheme approaches the same point as the unique solutions of the regularized problem, when the regularization parameter goes to 0. Furthermore this point can be characterized as the solution of a weighted minimum Euclidean norm problem. Finally several numerical experiments were performed in the field of rigid multibody dynamics supporting the theoretical claims.</p></abstract>

In this report we show that the iterated regularization scheme due to Riley and Golub, sometimes also called the iterated Tikhonov regularization, can be generalized to damped least squares problems where the weights matrix D is not necessarily the identity but a general symmetric and positive definite matrix. We show that the iterative scheme approaches the same point as the unique solutions of the regularized problem, when the regularization parameter goes to 0. Furthermore this point can be characterized as the solution of a weighted minimum Euclidean norm problem. Finally several numerical experiments were performed in the field of rigid multibody dynamics supporting the theoretical claims.

Iterative Solution of Weighted Linear Least Squares Problems

“Gheorghe Mihoc - Caius Iacob” Institute of Statistical Mathematics and Applied Mathematics

Friedrich-Alexander University of Erlangen-Nurnberg

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Iterative Solution of Weighted Linear Least Squares Problems"}

In this report we show that the iterated regularization scheme due to Riley and Golub, sometimes also called the iterated Tikhonov regularization, can be...

Iterative Solution of Weighted Linear Least Squares Problems

Published Online: Sep 22, 2020

Page range: 53 - 65

Received: Jul 10, 2019

Accepted: Dec 16, 2019

DOI: https://doi.org/10.2478/auom-2020-0019

Keywords
Weighted least squares problem, rigid body dynamics, generalized SVD, Tikhonov regularization, iterative solver

© 2020 Doina Carp et al., published by Sciendo

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

Iterative Solution of Weighted Linear Least Squares Problems

Published Online: Sep 22, 2020

Page range: 53 - 65

Received: Jul 10, 2019

Accepted: Dec 16, 2019

DOI: https://doi.org/10.2478/auom-2020-0019

KeywordsWeighted least squares problem, rigid body dynamics, generalized SVD, Tikhonov regularization, iterative solver

© 2020 Doina Carp et al., published by Sciendo

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

Keywords
Weighted least squares problem, rigid body dynamics, generalized SVD, Tikhonov regularization, iterative solver