Random Matrices Generating Large Growth in LU Factorization with Pivoting
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Publication:5150837
DOI10.1137/20M1338149zbMath1459.65036MaRDI QIDQ5150837
Nicholas J. Higham, Desmond J. Higham, Srikara Pranesh
Publication date: 15 February 2021
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Gaussian eliminationLU factorizationcomplete pivotingpartial pivotingHaar distributionrandom orthogonal matrixrook pivotinglarge growth factor
Random matrices (algebraic aspects) (15B52) Direct numerical methods for linear systems and matrix inversion (65F05)
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Uses Software
Cites Work
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- How to generate random matrices from the classical compact groups
- The singular values and vectors of low rank perturbations of large rectangular random matrices
- How many entries of a typical orthogonal matrix can be approximated by independent normals?
- Isotropic distributions of test matrices
- History and generality of the CS decomposition
- The Rook's pivoting strategy
- Euclidean distance between Haar orthogonal and Gaussian matrices
- Maxima of entries of Haar distributed matrices
- Superconcentration and Related Topics
- Average-Case Stability of Gaussian Elimination
- Error Analysis of Direct Methods of Matrix Inversion
- Iterative Refinement Implies Numerical Stability for Gaussian Elimination
- The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators
- On Deriving the Inverse of a Sum of Matrices
- Iterative refinement implies numerical stability
- Small-Sample Statistical Condition Estimates for General Matrix Functions
- Gaussian Elimination with Partial Pivoting Can Fail in Practice
- Uncertainty principles and ideal atomic decomposition
- 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
- A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error
- Large Growth Factors in Gaussian Elimination with Pivoting
- Accuracy and Stability of Numerical Algorithms
- Small-Sample Statistical Estimates for Matrix Norms
- Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems
- Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems
- Simulating Low Precision Floating-Point Arithmetic
- A Collection of Problems for Which Gaussian Elimination with Partial Pivoting is Unstable