A CONTRIBUTION TO THE CONDITIONING OF THE TOTAL LEAST-SQUARES PROBLEM

We derive closed formulas for the condition number of a linear function of the total least-squares solution. Given an overdetermined linear system Ax[approximate]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 pro...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2011-07, Vol.32 (3), p.685-699
Main Authors: BABOULIN, Marc, GRATTON, Serge
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Eigenvalues
Exact sciences and technology
Expected values
Linear algebra
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Sciences and techniques of general use
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Summary:We derive closed formulas for the condition number of a linear function of the total least-squares solution. Given an overdetermined linear system Ax[approximate]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. [PUBLICATION ABSTRACT]
ISSN:0895-4798
1095-7162
DOI:10.1137/090777608