Efficient algorithms for cur and interpolative matrix decompositions

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for implementation. For certain...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 43; no. 3; pp. 495 - 516
Main Authors Voronin, Sergey, Martinsson, Per-Gunnar
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2017
Springer Nature B.V
Subjects
Algorithms
Batch processing
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Decomposition
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Visualization
CUR
47N40
Approximation
15A23
65F30
Randomized algorithms
Low rank
Interpolative decomposition
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Summary:The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for implementation. For certain applications, further acceleration can be attained by incorporating techniques based on randomized projections. Numerical experiments demonstrate advantageous performance compared to existing techniques for computing CUR factorizations.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-016-9494-8