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
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Abstract	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.
AbstractList	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.
Author	Quintana‐Ortí, G. Martinsson, P. G. Heavner, N.
Author_xml	– sequence: 1 givenname: N. surname: Heavner fullname: Heavner, N. organization: Department of Applied Mathematics University of Colorado at Boulder Boulder Colorado USA – sequence: 2 givenname: P. G. orcidid: 0000-0002-1048-5270 surname: Martinsson fullname: Martinsson, P. G. organization: Department of Mathematics University of Texas at Austin Austin Texas USA – sequence: 3 givenname: G. orcidid: 0000-0002-7912-7826 surname: Quintana‐Ortí fullname: Quintana‐Ortí, G. organization: Departamento de Ingeniería y Ciencia de Computadores Universitat Jaume I Castellón Spain
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Snippet	This paper describes efficient algorithms for computing rank‐revealing factorizations of matrices that are too large to fit in main memory (RAM), and must... This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must...
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SubjectTerms	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
Title	Computing rank‐revealing factorizations of matrices stored out‐of‐core
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