Applications of Mathematics

, Volume 62, Issue 2, pp 105–120 | Cite as

Filter factors of truncated tls regularization with multiple observations

  • Iveta Hnětynková
  • Martin PlešingerEmail author
  • Jana Žáková


The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems Axb were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of A applied to b. This paper focuses on the situation when multiple observations b 1,..., b d are available, i.e., the T-TLS method is applied to the problem AXB, where B = [b 1,..., b d ] is a matrix. It is proved that the filtering representation of the T-TLS solution can be generalized to this case. The corresponding filter factors are explicitly derived.


truncated total least squares multiple right-hand sides eigenvalues of rank-d update ill-posed problem regularization filter factors 

MSC 2010

15A18 65F20 65F22 65F30 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  • Iveta Hnětynková
    • 1
  • Martin Plešinger
    • 2
    • 3
    Email author
  • Jana Žáková
    • 2
  1. 1.Charles UniversityFaculty of Mathematics and PhysicsPraha 2Czech Republic
  2. 2.Department of MathematicsTechnical University of LiberecLiberecCzech Republic
  3. 3.Institute of Computer Science of the Czech Academy of SciencesPraha 8Czech Republic

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