Simple backward error bounds for linear least-squares problems

DOI10.1016/j.laa.2013.03.007zbMath1281.65065OpenAlexW2062278821MaRDI QIDQ389595

David Titley-Peloquin, Serge Gratton, Pavel Jiránek

Publication date: 21 January 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2013.03.007

zbMATH Keywords

numerical examplesiterative algorithmslinear least squaresnormwise backward error

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (2)

LSMB: Minimizing the Backward Error for Least-Squares Problems ⋮ Estimating the backward error for the least-squares problem with multiple right-hand sides

Uses Software

• LSQR
• mctoolbox
• Blendenpik
• LSMR
• CRAIG

Cites Work

• Unnamed Item
• Faster least squares approximation
• Estimation of optimal backward perturbation bounds for the linear least squares problem
• Estimating the Backward Error in LSQR
• LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
• Blendenpik: Supercharging LAPACK's Least-Squares Solver
• Stopping Criteria for the Iterative Solution of Linear Least Squares Problems
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• New Fast Algorithms for Structured Linear Least Squares Problems
• Backward Perturbation Bounds for Linear Least Squares Problems
• Accuracy and Stability of Numerical Algorithms
• Optimal backward perturbation bounds for the linear least squares problem
• On the Accuracy of the Karlson--Waldén Estimate of the Backward Error for Linear Least Squares Problems
• Calculating the Singular Values and Pseudo-Inverse of a Matrix

This page was built for publication: Simple backward error bounds for linear least-squares problems