Geodesic
Filter factors of truncated TLS regularization with multiple observations
Applications of Mathematics, Tome 62 (2017) no. 2, pp. 105-120.

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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 $Ax\approx b$ 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 when multiple observations $b_1,\ldots ,b_d$ are available, i.e., the T-TLS method is applied to the problem $AX\approx B$, where $B=[b_1,\ldots ,b_d]$ 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.
DOI : 10.21136/AM.2017.0228-16
Classification : 15A18, 65F20, 65F22, 65F25, 65F30
Keywords: truncated total least squares; multiple right-hand sides; eigenvalues of rank-$d$ update; ill-posed problem; regularization; filter factors 
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     title = {Filter factors of truncated {TLS} regularization with multiple observations},
     journal = {Applications of Mathematics},
     pages = {105--120},
     publisher = {mathdoc},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0228-16/}
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Hnětynková, Iveta; Plešinger, Martin; Žáková, Jana. Filter factors of truncated TLS regularization with multiple observations. Applications of Mathematics, Tome 62 (2017) no. 2, pp. 105-120. doi : 10.21136/AM.2017.0228-16. http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0228-16/

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