Bounds for the Least Squares Residual using Scaled Total Least Squares

0404267 - UIVT-O 20020014 RIV DE eng C - Conference Paper (international conference)
Paige, C. C. - Strakoš, Zdeněk
Bounds for the Least Squares Residual using Scaled Total Least Squares.
Total Least Squares and Errors-in-Variables. Modelling: Analysis, Algorithms and Applications. Dordrecht: Kluwer Academic Publishers, 2002 - (van Huffel, S.; Lemmerling, P.), s. 35-43. ISBN 1-4020-0476-1.
[International Workshop on TLS and Errore-in-Variables Modelling. Leuven (BE), 27.08.2001-29.08.2001]
R&D Projects: GA AV ČR IAA2030801
Grant - others:NSERC(CA) OGP0009236
Institutional research plan: AV0Z1030915
Keywords : ordinary least squares * scaled total least squares * singular value decomposition * linear equations * least squares residual
Subject RIV: BA - General Mathematics

This contribution presents a theoretical analysis of the relationship between the sizes of the LS and Scaled TLS corrections (called the LS and Scaled TLS distances). We give new upper and lower bounds on the LS distance in terms of the Scaled TLS distance, compare these to existing bounds, and examine the tightness of the new bounds. This work can be applied to the analysis of iterative methods which minimize the residual norm.
Permanent Link: http://hdl.handle.net/11104/0124530