Abstract
The singular value decomposition (SVD) of a data matrix is useful for providing rank and subspace information as well as solving and analyzing total least squares (TLS) problems. Rank-revealing decompositions, herein referred to as UTV decompositions, and Lanczos methods have been proposed as substitutes for the SVD in various applications through the years. These type of methods are appropriate for solving TLS-related problems because they can efficiently and reliably provide an orthogonal basis that accurately approximates the needed numerical row space or null space.
The development and availability of reliable and robust codes for TLS algorithms always lags the pace of the literature. We discuss some recent developments in the use of UTV decompositions and Lanczos methods for solving TLS-related problems along with related Matlab codes.
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Fierro, R.D., Hansen, P.C. (2002). Recent Developments in Rank Revealing and Lanczos Methods for TLS-Related Problems. In: Van Huffel, S., Lemmerling, P. (eds) Total Least Squares and Errors-in-Variables Modeling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3552-0_5
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DOI: https://doi.org/10.1007/978-94-017-3552-0_5
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