Condition numbers and backward perturbation bound for linear matrix equations
From MaRDI portal
Publication:2889376
DOI10.1002/nla.725zbMath1249.15006OpenAlexW2098271661MaRDI QIDQ2889376
Hua Dai, Qing-Quan He, Xing-Dong Yang
Publication date: 7 June 2012
Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nla.725
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Matrix equations and identities (15A24) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)
Related Items (3)
Condition numbers of the least squares problems with multiple right-hand sides ⋮ Structured backward error analysis for generalized saddle point problems ⋮ Structured condition number for multiple right-hand side linear systems with parameterized quasiseparable coefficient matrix
Uses Software
Cites Work
- Unnamed Item
- On optimal backward perturbation bounds for the linear least squares problem
- On the symmetric solutions of linear matrix equations
- Componentwise perturbation theory for linear systems with multiple right- hand sides
- Compatibility of approximate solutions of inaccurate linear equations
- Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems
- Backward error bounds for constrained least squares problems
- Structured backward errors for KKT systems
- Backward perturbation analysis of certain characteristic subspaces
- Condition numbers and their condition numbers
- Structured backward error and condition number for linear systems of the type \(A^* Ax = b\)
- Condition numbers for structured least squares problems
- Mixed, Componentwise, and Structured Condition Numbers
- A note on backward errors for structured linear systems
- Backward Error and Condition of Structured Linear Systems
- The Strong Stability of Algorithms for Solving Symmetric Linear Systems
- Bounds for the Structured Backward Errors of Vandermonde Systems
- Backward Perturbation Bounds for Linear Least Squares Problems
- Optimal Backward Perturbation Bounds for Underdetermined Systems
- Structured Perturbations Part I: Normwise Distances
- Structured Perturbations Part II: Componentwise Distances
- Accuracy and Stability of Numerical Algorithms
- Optimal backward perturbation bounds for the linear least squares problem
- Optimal backward perturbation bounds for the linear least-squares problem with multiple right-hand sides
- A Theory of Condition
- On Error Bounds for Generalized Inverses
- On the Compatibility of a Given Solution With the Data of a Linear System
This page was built for publication: Condition numbers and backward perturbation bound for linear matrix equations