Filter factors of truncated TLS regularization with multiple observations

Hnětynková, Iveta, Plešinger, Martin, and Žáková, Jana. "Filter factors of truncated TLS regularization with multiple observations." Applications of Mathematics 62.2 (2017): 105-120. <http://eudml.org/doc/287936>.

@article{Hnětynková2017,
abstract = {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.},
author = {Hnětynková, Iveta, Plešinger, Martin, Žáková, Jana},
journal = {Applications of Mathematics},
keywords = {truncated total least squares; multiple right-hand sides; eigenvalues of rank-$d$ update; ill-posed problem; regularization; filter factors},
language = {eng},
number = {2},
pages = {105-120},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Filter factors of truncated TLS regularization with multiple observations},
url = {http://eudml.org/doc/287936},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Hnětynková, Iveta
AU - Plešinger, Martin
AU - Žáková, Jana
TI - Filter factors of truncated TLS regularization with multiple observations
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 105
EP - 120
AB - 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.
LA - eng
KW - truncated total least squares; multiple right-hand sides; eigenvalues of rank-$d$ update; ill-posed problem; regularization; filter factors
UR - http://eudml.org/doc/287936
ER -