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

• ID: 2606, RIV: 10103996
• ISSN: 0895-4798, ISBN: not specified
• source: SIAM Journal on Matrix Analysis and Applications
• keywords: total least squares; multiple right-hand sides; linear approximation problems
• authors: Iveta Hnětynková, Martin Plešinger, Diana Maria Sima, Zdeněk Strakoš, Sabine Van Huffel
• authors from KNM: Strakoš Zdeněk, Hnětynková Iveta

Abstract

The paper investigates the analysis of the total least squares (TLS) problem with multiple right-hand sides. It reviews the classical analysis of the existence and uniqueness of the TLS solution given by Sabine Van Huffel and Joos Vandewalle, SIAM Publications, Philadelphia, 1991. This analysis, unfortunately, does not cover all the situations that can occur in the multiple right-hand side case. This paper introduces a new complete classification of all linear approximation problems with multiple right-hand sides of the form AX~B which is based on properties of singular value decomposition of the extended matrix [B|A].