.png){kind=icon}
.png){kind=icon}
Return
Randomized numerical linear algebra: Foundations and algorithms
.png){kind=icon}
OA
AI
DOI：10.1017/S0962492920000021.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This survey describes probabilistic algorithms for linear algebraic computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problems. The paper treats both the theoretical foundations of the subject and practical computational issues. Topics include norm estimation, matrix approximation by sampling, structured and unstructured random embeddings, linear regression problems, low-rank approximation, subspace iteration and Krylov methods, error estimation and adaptivity, interpolatory and CUR factorizations, Nystrom approximation of positive semidefinite matrices, single-view ('streaming') algorithms, full rank-revealing factorizations, solvers for linear systems, and approximation of kernel matrices that arise in machine learning and in scientific computing.
Keywords:
MONTE-CARLO ALGORITHMS
REVEALING QR FACTORIZATION
JOHNSON-LINDENSTRAUSS
GAUSSIAN-ELIMINATION
EFFICIENT ALGORITHMS
MATRIX APPROXIMATION
LARGEST EIGENVALUE
CONDITION NUMBERS
SAMPLING METHODS
CONVEX-PROGRAMS
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
11.3
Papers:
89
Citations:
3.4K