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

DOI10.1007/s10543-009-0213-4zbMath1168.65022OpenAlexW2116485776MaRDI QIDQ1014905

Marc Baboulin, Serge Gratton

Publication date: 29 April 2009

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-009-0213-4

zbMATH Keywords

numerical examplecondition numbersadjoint operatordual normcomponentwise perturbationslinear least squares solution

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)

Related Items

Backward error and condition number analysis for the indefinite linear least squares problem, Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem, Condition numbers of the least squares problems with multiple right-hand sides, On the partial condition numbers for the indefinite least squares problem, A note on stable perturbations of Moore–Penrose inverses, On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products, Condition numbers for a linear function of the solution to the constrained and weighted least squares problem and their statistical estimation, A condition analysis of the weighted linear least squares problem using dual norms, On condition numbers for least squares with quadric inequality constraint, Condition numbers for a linear function of the solution of the linear least squares problem with equality constraints, Structured condition numbers of structured Tikhonov regularization problem and their estimations, On the condition number theory of the equality constrained indefinite least squares problem

Uses Software

• LAPACK
• CLAPACK
• BLAS
• mctoolbox

Cites Work

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• Zusammenfassender Bericht. Genauigkeitsfragen bei der Lösung linearer Gleichungssysteme