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RANDOMIZED NYSTRÖM PRECONDITIONING.
- Source :
-
SIAM Journal on Matrix Analysis & Applications . 2023, Vol. 44 Issue 2, p718-752. 35p. - Publication Year :
- 2023
-
Abstract
- This paper introduces the Nyström preconditioned conjugate gradient (PCG) algorithm for solving a symmetric positive-definite linear system. The algorithm applies the randomized Nyström method to form a low-rank approximation of the matrix, which leads to an efficient preconditioner that can be deployed with the conjugate gradient algorithm. Theoretical analysis shows that the preconditioned system has constant condition number as soon as the rank of the approximation is comparable with the number of effective degrees of freedom in the matrix. The paper also develops adaptive methods that provably achieve similar performance without knowledge of the effective dimension. Numerical tests show that Nyström PCG can rapidly solve large linear systems that arise in data analysis problems, and it surpasses several competing methods from the literature. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LOW-rank matrices
*DEGREES of freedom
*DATA analysis
Subjects
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 44
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 169719916
- Full Text :
- https://doi.org/10.1137/21M1466244