Level choice in truncated total least squares

The method of truncated total least squares (TTLS) is an alternative to the classical truncated singular value decomposition (TSVD) used for the regularization of ill-conditioned linear systems. Truncation methods aim at limiting the contribution of noise or rounding errors by cutting off a certain number of terms in an expansion such as the singular value decomposition. To this end a truncation level k must be carefully chosen. The TTLS solution becomes more significantly dominated by noise or errors when the truncation level k is overestimated than the TSVD solution does. Model selection methods that are often applied in the context of the TSVD are modified to be applied in the context of the TTLS. The proposed modified generalized cross validation (GCV) combined with the TTLS method performs better than the classical GCV combined with the TSVD, especially, when both the coefficient matrix and the right-hand side are contaminated by noise.