A contribution to the conditioning of the total least squares problem

We derive closed formulas for the condition number of a linear function of the total least squares solution. Given an over determined linear system Ax = b, we show that this condition number can be computed using the singular values and the right singular vectors of [A, b] and A. We also provide an upper bound that requires the computation of the largest and the smallest singular value of [A, b] and the smallest singular value of A. In numerical examples, we compare these values and the resulting forward error bounds with the error estimates given in [17].