Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems

DOI10.1137/18M1229511zbMath1420.65017MaRDI QIDQ5230659

Mawussi Zounon, Nicholas J. Higham, Srikara Pranesh

Publication date: 28 August 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

linear systempreconditioningiterative refinementdiagonal scalingoverflowmixed precisionunderflowgmreshalf precision arithmeticFP16subnormal numbers

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Preconditioners for iterative methods (65F08)

Related Items

Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores, Mixed precision algorithms in numerical linear algebra, Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations, A Note on Inexact Inner Products in GMRES, 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, Numerical stability of algorithms at extreme scale and low precisions, GMRES algorithms over 35 years, Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores, Random Matrices Generating Large Growth in LU Factorization with Pivoting, Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems, The physics of numerical analysis: a climate modelling case study, Numerical algorithms for high-performance computational science, Simulating Low Precision Floating-Point Arithmetic, Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems, Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization, Newton's Method in Mixed Precision

Uses Software

• LAPACK
• SparseMatrix
• mctoolbox
• Algorithm 978

Cites Work

• Unnamed Item
• Scaling linear optimization problems prior to application of the simplex method
• A Symmetry Preserving Algorithm for Matrix Scaling
• More reliable forecasts with less precise computations: a fast-track route to cloud-resolved weather and climate simulators?
• The university of Florida sparse matrix collection
• Max-Balanced Hungarian Scalings
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• On scaling linear programs—some experimental results
• LAPACK Users' Guide
• Faster numerical algorithms via exception handling
• Algorithm 978
• 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