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A contribution to the conditioning of the total least squares problem

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.
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https://hal.inria.fr/inria-00546886
Contributor : Marc Baboulin <>
Submitted on : Saturday, December 25, 2010 - 8:27:28 AM
Last modification on : Thursday, April 8, 2021 - 9:06:03 AM
Long-term archiving on: : Saturday, March 26, 2011 - 2:21:11 AM

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  • HAL Id : inria-00546886, version 1
  • ARXIV : 1012.5484

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Marc Baboulin, Serge Gratton. A contribution to the conditioning of the total least squares problem. [Research Report] RR-7488, INRIA. 2010. ⟨inria-00546886⟩

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