Condition numbers for the truncated total least squares problem and their estimations

On the condition number of the total least squares problem

Condition Numbers for Structured Least Squares Problems

This paper studies the normwise perturbation theory for structured least squares problems. The structures under investigation are symmetric, persymmetric, skewsymmetric, Toeplitz and Hankel. We present the condition numbers for structured least squares. AMS subject classification (2000): 15A18, 65F20, 65F25, 65F50.

Level choice in truncated total least squares

The method of truncated total least squares [2] is an alternative to the classical truncated singular value decomposition used for the regularization of ill-conditioned linear systems Ax ≈ b [3]. 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 truncati...

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 matrix and the right-hand side are not precisely known. This paper focuses on the use of TLS for solving problems with very ill-conditioned coefficient matrices whose singular values decay...

Sensitivity and Conditioning of the Truncated Total Least Squares Solution

We present an explicit expression for the condition number of the truncated total least squares (TLS) solution of Ax ≈ b. This expression is obtained using the notion of the Fréchet derivative. We also give upper bounds on the condition number which are simple to compute and interpret. These results generalize those in the literature for the untruncated TLS problem. Numerical experiments demons...