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 demonstrate that our bounds are often a very good estimate of the condition number, and provide a significant improvement to known bounds.