Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems
From MaRDI portal
Publication:5856681
DOI10.1137/20M1316822zbMath1461.65032OpenAlexW3006375150MaRDI QIDQ5856681
Erin Claire Carson, Nicholas J. Higham, Srikara Pranesh
Publication date: 29 March 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/20m1316822
preconditioningGMRESleast squaresMINRESiterative refinementmixed precision arithmetichalf precision arithmetic
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)
Related Items
Mixed precision algorithms in numerical linear algebra, A Computational Study of Using Black-box QR Solvers for Large-scale Sparse-dense Linear Least Squares Problems, Mixed Precision Iterative Refinement with Sparse Approximate Inverse Preconditioning, Five-Precision GMRES-Based Iterative Refinement, Double precision is not necessary for LSQR for solving discrete linear ill-posed problems, Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems, Numerical algorithms for high-performance computational science, Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, Solving large linear least squares problems with linear equality constraints
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Iterative refinement enhances the stability of \(QR\) factorization methods for solving linear equations
- The worst-case GMRES for normal matrices
- Numerical methods for solving linear least squares problems
- Note on the iterative refinement of least squares solution
- A Note on Preconditioning Nonsymmetric Matrices
- The university of Florida sparse matrix collection
- An Augmented Stability Result for the Lanczos Hermitian Matrix Tridiagonalization Process
- A Note on GMRES Preconditioned by a Perturbed $L D L^T$ Decomposition with Static Pivoting
- Solution of Sparse Indefinite Systems of Linear Equations
- A Note on Preconditioning for Indefinite Linear Systems
- A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems
- Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions
- Accuracy and Stability of Numerical Algorithms
- On the cost of iterative computations
- Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems
- Simulating Low Precision Floating-Point Arithmetic
- Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES
- Iterative refinement of linear least squares solutions I
