2010/12/25 by Marc Baboulin, Baboulin, Marc, Gratton, Serge
Computer Science · Engineering · Mathematics · #Control Systems and Identification #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Statistical and numerical algorithms
paper · doi:10.48550/arxiv.1012.5484
openalex publication_date 2010/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.