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Applied Mathematics Letters
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Applied Mathematics Letters
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Tikhonov regularization for weighted total least squares problems

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2007 English Publisher:Elsevier BVJournal:Applied Mathematics Letters, volume 20, pages 82-87 (issn: 0893-9659, Copyright policy )
Authors: Yimin Wei 0001; Naimin Zhang; Michael K. Ng 0001; Wei Xu;

doi: 10.1016/j.aml.2006.03.004

Tikhonov regularization for weighted total least squares problems

Abstract

A general version of Tikhonov's formulation for the linear weighted total least squares (WTLS) problem has been considered by \textit{G. H. Golub} and \textit{C. F. van Loan} [SIAM J. Numer. Anal. 17, 883--893 (1980; Zbl 0468.65011)]. The present paper focus on the regularized weighted total least squares (RWTLS) formulation. It is shown that the RWTLS solution is closely related to the Tikhonov solution to the WTLS problem. By converting the RWTLS problem into an equivalent augmented system, the solution can be obtained by a tridiagonal solver.

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Keywords

Total least squares, Ill-posedness and regularization problems in numerical linear algebra, Weighted regularized total least squares, Tikhonov regularization, Applied Mathematics, weighted regularized total least squares, Lagrange multiplier, total least squares, Matrix differentiation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
12
Average
Top 10%
Average
hybrid
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