Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution

We prove duality results for adjoint operators and product norms in the framework of Euclidean spaces. We show how these results can be used to derive condition numbers especially when perturbations on data are measured componentwise relatively to the original data. We apply this technique to obtain...

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Bibliographic Details
Published in:BIT (Lisse : trykt utg.) 2009-03, Vol.49 (1), p.3-19
Main Authors: Baboulin, Marc, Gratton, Serge
Format: Article
Language:English
Subjects:
adjoint operator
componentwise perturbations
Computational Mathematics and Numerical Analysis
condition number
Differential geometry
dual norm
Exact sciences and technology
Geometry
linear least squares
Mathematics
Mathematics and Statistics
Numeric Computing
numerisk lineær algebra
Sciences and techniques of general use
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Summary:We prove duality results for adjoint operators and product norms in the framework of Euclidean spaces. We show how these results can be used to derive condition numbers especially when perturbations on data are measured componentwise relatively to the original data. We apply this technique to obtain formulas for componentwise and mixed condition numbers for a linear function of a linear least squares solution. These expressions are closed when perturbations of the solution are measured using a componentwise norm or the infinity norm and we get an upper bound for the Euclidean norm.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-009-0213-4