A contribution to the conditioning of the total least squares problem
Numerical Analysis
2010-12-30 v1
Abstract
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 existing error estimates.
Keywords
Cite
@article{arxiv.1012.5484,
title = {A contribution to the conditioning of the total least squares problem},
author = {Marc Baboulin and Serge Gratton},
journal= {arXiv preprint arXiv:1012.5484},
year = {2010}
}