Filter factors of truncated tls regularization with multiple observations

• ID: 2771, RIV: 10366649
• ISSN: 0862-7940, ISBN: not specified
• source: Applications of Mathematics
• keywords: truncated total least squares; multiple right-hand sides; eigenvalues of rank-d update; ill-posed problem; regularization; filter factors
• authors: Iveta Hnětynková, Martin Plešinger, Jana Žáková
• authors from KNM: Hnětynková Iveta

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 ~ 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),..., b (d) are available, i.e., the T-TLS method is applied to the problem AX ~ B, 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.