Computing rank‐revealing factorizations of matrices stored out‐of‐core

This paper describes efficient algorithms for computing rank‐revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out‐of‐core or out‐of‐memory). Traditional algorithms for computing rank‐reveali...

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Veröffentlicht in:Concurrency and computation Jg. 35; H. 22
Hauptverfasser: Heavner, N., Martinsson, P. G., Quintana‐Ortí, G.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken Wiley Subscription Services, Inc 10.10.2023
Wiley
Schlagworte:
Algorithms
blocked matrix computations
Computation
Computer Science
Data processing
Factorization
householder QR factorization
HQRRP factorization
Mathematical analysis
Matrices (mathematics)
Memory devices
out-of-core computation
partial rank-revealing factorization
Random access memory
randomized numerical linear algebra
randUTV factorization
rank-revealing factorization
shared-memory multicore processors
shared-memory multiprocessors
Singular value decomposition
ISSN:1532-0626, 1532-0634, 1532-0634
Online-Zugang:Volltext
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Zusammenfassung:This paper describes efficient algorithms for computing rank‐revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out‐of‐core or out‐of‐memory). Traditional algorithms for computing rank‐revealing factorizations (such as the column pivoted QR factorization and the singular value decomposition) are very communication intensive as they require many vector‐vector and matrix‐vector operations, which become prohibitively expensive when data is not in RAM. Randomization allows to reformulate new methods so that large contiguous blocks of the matrix are processed in bulk. The paper describes two distinct methods. The first is a blocked version of column pivoted Householder QR, organized as a “left‐looking” method to minimize the number of the expensive write operations. The second method results employs a UTV factorization. It is organized as an algorithm‐by‐blocks to overlap computations and I/O operations. As it incorporates power iterations, it is much better at revealing the numerical rank. Numerical experiments on several computers demonstrate that the new algorithms are almost as fast when processing data stored on slow memory devices as traditional algorithms are for data stored in RAM.
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USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
National Science Foundation (NSF)
SC0022251
Spanish Ministry of Science and Innovation and the Research State Agency
US Department of the Navy, Office of Naval Research (ONR)
ISSN:1532-0626
1532-0634
1532-0634
DOI:10.1002/cpe.7726