Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution
type: Item
instance of: scholarly article
title: Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution
zbMATH Open document ID: 1168.65022
author: Marc Baboulin
author: Serge Gratton
published in: BIT
publication date: 2009-04-29T00:00:00Z
review text: Duality results for adjoint operators and product norms in the framework of Euclidean space are proved. It is shown how these results can be used to derive condition numbers especially when perturbations on data are measured componentwise relatively to the original data. The technique proposed is applied 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 an upper bound for the Euclidean norm is got. A numerical example is given.
reviewed by: Petko Hr. Petkov
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 5549603
zbMATH Keywords: dual norm
zbMATH Keywords: adjoint operator
zbMATH Keywords: componentwise perturbations
zbMATH Keywords: condition numbers
zbMATH Keywords: linear least squares solution
zbMATH Keywords: numerical example
describes a project that uses: LAPACK
describes a project that uses: mctoolbox
describes a project that uses: CLAPACK
describes a project that uses: BLAS
MaRDI profile type: Publication
full work available at URL: s10543-009-0213-4
OpenAlex ID: W2116485776
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DOI: 10.1007/S10543-009-0213-4
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description: scientific article; zbMATH DE number 5549603