New studies of randomized augmentation and additive preprocessing

DOI10.1016/j.laa.2016.09.035zbMath1353.65033arXiv1412.5864OpenAlexW2963304612MaRDI QIDQ332656

Mohammad Hasan, M. Dambrine

Publication date: 8 November 2016

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

Full work available at URL: https://arxiv.org/abs/1412.5864

zbMATH Keywords

dualityill-conditioned matrixGaussian random matricesderandomizationsingular valuelow-rank approximationfundamental matrix computationrandomized matrix algorithmssingular subspaces of a matrixsparse and structured preprocessors

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10) Random matrices (algebraic aspects) (15B52)

Related Items

Numerically safe Gaussian elimination with no pivoting, Sublinear Cost Low Rank Approximation via Subspace Sampling, CUR LRA at Sublinear Cost Based on Volume Maximization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• Solving linear systems of equations with randomization, augmentation and aggregation
• Matrix computations and polynomial root-finding with preprocessing
• Additive preconditioning for matrix computations
• Additive preconditioning, eigenspaces, and the inverse iteration
• Randomized preprocessing of homogeneous linear systems of equations
• Determinantal rings
• On perturbation bounds for the QR factorization
• A theory of pseudoskeleton approximations
• On the existence and computation of rank-revealing LU factorizations
• Randomized preprocessing versus pivoting
• Random multipliers numerically stabilize Gaussian and block Gaussian elimination: proofs and an extension to low-rank approximation
• Schur aggregation for linear systems and determinants
• Additive preconditioning and aggregation in matrix computations
• Effect of small rank modification on the condition number of a matrix
• Estimating the norms of random circulant and Toeplitz matrices and their inverses
• IMPROVED ANALYSIS OF THE SUBSAMPLED RANDOMIZED HADAMARD TRANSFORM
• Random matrix theory
• Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices
• Additive Preconditioning for Matrix Computations
• Eigenvalues and Condition Numbers of Random Matrices
• On Rank-Revealing Factorisations
• Accuracy and Stability of Numerical Algorithms
• Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
• Tails of Condition Number Distributions
• Condition Numbers of Gaussian Random Matrices
• Homotopic residual correction processes