Abstract
We derive closed formulas for the condition number of a linear function of the total least-squares solution. Given an overdetermined 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 by Van Huffel and Vandewalle [The Total Least Squares Problem: Computational Aspects and Analysis, Frontiers Appl. Math. 9, SIAM, Philadelphia, 1991], and we show the limitation of the first order approach.
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