Iterative Solution of Weighted Linear Least Squares Problems

Carp D, Popa C, Preclik T, Rüde U (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Ovidius University, Constanta

Book Volume: 28

Pages Range: 53-65

Journal Issue: 2

DOI: 10.2478/auom-2020-0019

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.

Authors with CRIS profile

Tobias Preclik Lehrstuhl für Informatik 10 (Systemsimulation) Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation)

Involved external institutions

Ovidius University of Constanta RO Romania (RO) Politechnic University of Bucharest / Universitatea Politehnica din București RO Romania (RO)

How to cite

APA:

Carp, D., Popa, C., Preclik, T., & Rüde, U. (2020). Iterative Solution of Weighted Linear Least Squares Problems. Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica, 28(2), 53-65. https://doi.org/10.2478/auom-2020-0019

MLA:

Carp, Doina, et al. "Iterative Solution of Weighted Linear Least Squares Problems." Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica 28.2 (2020): 53-65.

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