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• W2798351323 abstract "This paper describes practical randomized algorithms for low-rank matrix approximation that accommodate any budget for the number of views of the matrix. The presented algorithms, which are aimed at being as pass efficient as needed, expand and improve on popular randomized algorithms targeting efficient low-rank reconstructions. First, a more flexible subspace iteration algorithm is presented that works for any views $v geq 2$, instead of only allowing an even $v$. Secondly, we propose more general and more accurate single-pass algorithms. In particular, we propose a more accurate memory efficient single-pass method and a more general single-pass algorithm which, unlike previous methods, does not require prior information to assure near peak performance. Thirdly, combining ideas from subspace and single-pass algorithms, we present a more pass-efficient randomized block Krylov algorithm, which can achieve a desired accuracy using considerably fewer views than that needed by a subspace or previously studied block Krylov methods. However, the proposed accuracy enhanced block Krylov method is restricted to large matrices that are either accessed a few columns or rows at a time. Recommendations are also given on how to apply the subspace and block Krylov algorithms when estimating either the dominant left or right singular subspace of a matrix, or when estimating a normal matrix, such as those appearing in inverse problems. Computational experiments are carried out that demonstrate the applicability and effectiveness of the presented algorithms." @default.
• W2798351323 created "2018-05-07" @default.
• W2798351323 creator A5055749362 @default.
• W2798351323 date "2018-04-20" @default.
• W2798351323 modified "2023-09-27" @default.
• W2798351323 title "Pass-Efficient Randomized Algorithms for Low-Rank Matrix Approximation Using Any Number of Views" @default.
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• W2798351323 hasPublicationYear "2018" @default.
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