Filter Factors of Truncated TLS Regularization with Multiple Observations

0474150 - ÚI 2018 RIV CZ eng J - Journal Article
Hnětynková, I. - Plešinger, Martin - Žáková, J.
Filter Factors of Truncated TLS Regularization with Multiple Observations.
Applications of Mathematics. Roč. 62, č. 2 (2017), s. 105-120. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : truncated total least squares * multiple right-hand sides * eigenvalues of rank-d update * ill-posed problem * regularization * filter factors
OECD category: Applied mathematics
Impact factor: 0.897, year: 2017
http://hdl.handle.net/10338.dmlcz/146698

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 b1,..., bd are available, i.e., the T-TLS method is applied to the problem AX approx B, where B = [b1,..., bd] 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.
Permanent Link: http://hdl.handle.net/11104/0271259