Randomized block Krylov methods for approximating extreme eigenvalues
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Publication:2068363
DOI10.1007/s00211-021-01250-3zbMath1480.65086arXiv2110.00649OpenAlexW3202475252MaRDI QIDQ2068363
Publication date: 19 January 2022
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2110.00649
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Random matrices (probabilistic aspects) (60B20) Randomized algorithms (68W20)
Uses Software
Cites Work
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- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Convergence of the block Lanczos method for eigenvalue clusters
- On the optimality of Krylov information
- A randomized algorithm for the decomposition of matrices
- The rate of convergence of conjugate gradients
- Invertibility of ``large submatrices with applications to the geometry of Banach spaces and harmonic analysis
- On optimality of Krylov's information when solving linear operator equations
- On the randomized error of polynomial methods for eigenvector and eigenvalue estimates
- Latent semantic indexing: A probabilistic analysis
- Numerical Methods for Large Eigenvalue Problems
- An Algorithm for the Principal Component Analysis of Large Data Sets
- Low-Rank Matrix Approximations Do Not Need a Singular Value Gap
- Estimating Extremal Eigenvalues and Condition Numbers of Matrices
- A Randomized Algorithm for Principal Component Analysis
- On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
- Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a Random Start
- Probabilistic Bounds on the Extremal Eigenvalues and Condition Number by the Lanczos Algorithm
- Templates for the Solution of Algebraic Eigenvalue Problems
- Estimating a largest eigenvector by Lanczos and polynomial algorithms with a random start
- Tight query complexity lower bounds for PCA via finite sample deformed wigner law
- Subspace Iteration Randomization and Singular Value Problems
- Convergence of Polynomial Restart Krylov Methods for Eigenvalue Computations
- Structural Convergence Results for Approximation of Dominant Subspaces from Block Krylov Spaces
- Fast monte-carlo algorithms for finding low-rank approximations
- Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
- The Lanczos and Conjugate Gradient Algorithms
- GMRES Convergence Analysis for a Convection-Diffusion Model Problem
- Exponential integral integral infinity 1 e-xtt -ndt for large values of n
- Randomized numerical linear algebra: Foundations and algorithms