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Reports (Research Report) Year : 2010

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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Dates and versions

inria-00546886 , version 1 (25-12-2010)

Identifiers

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

Cite

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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