Computing the conditioning of the components of a linear least-squares solution

DOI10.1002/nla.627zbMath1224.65104arXiv0710.0829OpenAlexW2019358395MaRDI QIDQ3011686

Serge Gratton, Marc Baboulin, Julien Langou, Jack J. Dongarra

Publication date: 29 June 2011

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.0829

zbMATH Keywords

numerical exampleparameter estimationcondition numberconditioningvariance-covariance matrix\texttt{LAPACK}\texttt{ScaLAPACK}mass of jupiteroverdetermined full rank linear least-squares problemspace geodesystatistical linear least squares

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical solutions to equations with linear operators (65J10) Galactic and stellar structure (85A15) Geodesy, mapping problems (86A30) Conditioning of matrices (15A12)

Related Items (7)

Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems ⋮ Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations ⋮ Computing Least Squares Condition Numbers on Hybrid Multicore/GPU Systems ⋮ A note on stable perturbations of Moore–Penrose inverses ⋮ On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products ⋮ Mixed, componentwise condition numbers and small sample statistical condition estimation of Sylvester equations ⋮ Structured condition numbers of structured Tikhonov regularization problem and their estimations

Uses Software

• LAPACK
• NAG
• ScaLAPACK
• mctoolbox
• VanHuffel

Cites Work

• Unnamed Item
• An Analysis of the Total Least Squares Problem
• A contribution to the theory of condition
• On the condition number of linear least squares problems in a weighted Frobenius norm
• Condition Estimates
• LAPACK Users' Guide
• Statistical Condition Estimation for Linear Least Squares
• On the Sensitivity of Solution Components in Linear Systems of Equations
• ScaLAPACK Users' Guide
• Accuracy and Stability of Numerical Algorithms

This page was built for publication: Computing the conditioning of the components of a linear least-squares solution