1. bookVolume 28 (2020): Issue 2 (July 2020)
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17 May 2013
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access type Open Access

Iterative Solution of Weighted Linear Least Squares Problems

Published Online: 22 Sep 2020
Page range: 53 - 65
Received: 10 Jul 2019
Accepted: 16 Dec 2019
Journal Details
License
Format
Journal
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English

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.

Keywords

MSC 2010

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