Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

The total least squares problem in AX=B. A new classification with the relationship to the classical works

by I. Hnetynkova and M. Plesinger and D. M. Sima and Z. Strakos and S. Van Huffel

(Report number 2010-38)

Abstract
The presented paper revisits the analysis of the total least squares (TLS) problem $AX/approx B$ with multiple right-hand sides given by Sabine Van Huffel and Joos Vandewalle, in the monograph: The Total Least Squares Problem: Computational Aspects and Analysis, SIAM Publications, Philadelphia 1991. The newly proposed classification is based on properties of the singular value decomposition of the extended matrix $(BIA)$. It aims at identifying the cases when a TLS solution does or does not exist, and when the output computed by the classical TLS algorithm, given by Van Huffel and Vandewalle, is actually a TLS solution. The presented results on existence and uniqueness of the TLS solution reveal subtleties that were not captured in the known literature.

Keywords: total least squares (TLS), multiple right-hand sides, linear approximation problems, orthogonally invariant problems, orthogonal regression, errors-in-variables modeling

@Techreport{HPSSV10_438,
  author = {I. Hnetynkova and M. Plesinger and D. M. Sima and Z. Strakos and S. Van Huffel},
  title = {The total least squares problem in AX=B. A new classification with the relationship to the classical works},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2010-38},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-38.pdf },
  year = {2010}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).