The Core Problem within a Linear Approximation Problem $AX/approx B$ with Multiple Right-Hand Sides

0426569 - ÚI 2014 RIV US eng J - Journal Article
Hnětynková, Iveta - Plešinger, Martin - Strakoš, Z.
The Core Problem within a Linear Approximation Problem $AX/approx B$ with Multiple Right-Hand Sides.
SIAM Journal on Matrix Analysis and Applications. Roč. 34, č. 3 (2013), s. 917-931. ISSN 0895-4798. E-ISSN 1095-7162
R&D Projects: GA ČR GA13-06684S
Grant - others:GA ČR(CZ) GA201/09/0917; GA MŠk(CZ) EE2.3.09.0155; GA MŠk(CZ) EE2.3.30.0065
Program: GA
Institutional support: RVO:67985807
Keywords : total least squares problem * multiple right-hand sides * core problem * linear approximation problem * error-in-variables modeling * orthogonal regression * singular value decomposition
Subject RIV: BA - General Mathematics
Impact factor: 1.806, year: 2013

This paper focuses on total least squares (TLS) problems $AX/approx B$ with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnětynková et al., SIAM J. Matrix Anal. Appl., 32, 2011, pp. 748--770]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakoš, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861--875] showed how necessary and sufficient information for solving $Ax/approx b$ can be revealed from the original data through the so-called core problem concept. In this paper we present a theoretical study extending this concept to problems with multiple right-hand sides. The data reduction we present here is based on the singular value decomposition of the system matrix $A$. We show minimality of the reduced problem; in this sense the situation is analogous to the single right-hand side case. Some other properties of the core problem, however, cannot be extended to the case of multiple right-hand sides.
Permanent Link: http://hdl.handle.net/11104/0232296