Randomized numerical linear algebra: Foundations and algorithms
| Autor: | Joel A. Tropp, Per-Gunnar Martinsson |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Numerical linear algebra Computer science General Mathematics Linear system 010103 numerical & computational mathematics Positive-definite matrix computer.software_genre 01 natural sciences 010104 statistics & probability Matrix (mathematics) Norm (mathematics) Probabilistic analysis of algorithms 0101 mathematics Algebraic number computer Algorithm Subspace topology |
| Zdroj: | Acta Numerica. 29:403-572 |
| ISSN: | 1474-0508 0962-4929 |
| Popis: | 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, Nyström 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. |
| Databáze: | OpenAIRE |
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