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Filter factors of truncated TLS regularization with multiple observations

Iveta Hnětynková;  Martin Plešinger;  Jana Žáková — 2017

Applications of Mathematics

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 A x ≈ b 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...

Solvability classes for core problems in matrix total least squares minimization

Iveta Hnětynková;  Martin Plešinger;  Jana Žáková — 2019

Applications of Mathematics

Linear matrix approximation problems A X ≈ B are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if B is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of B is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...

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