REGULARIZATION BY TRUNCATED TOTAL LEAST-SQUARES

The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications . The TLS method is suited to problems in which both the coefficient m atrix and the right-hand side are got precisely known. This paper focu ses on the use of TLS for solving problems with very ill-conditioned c oefficient matrices whose singular values decay gradually (so-called d iscrete ill-posed problems), where some regularization is necessary to stabilize the computed solution. We filter the solution by truncating the small singular values of the TLS matrix. We express our results i n terms of the singular value decomposition (SVD) of the coefficient m atrix rather than the augmented matrix. This leads to insight into the filtering properties of the truncated TLS method as compared to regul arized least squares solutions. In addition, we propose and test an it erative algorithm based on Lanczos bidiagonalization for computing tru ncated TLS solutions.