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- Vladimir Rokhlin, Arthur Szlam, Mark Tygert
- SIAM J. Matrix Analysis Applications
- 2009

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any… (More)

- Edo Liberty, Franco Woolfe, Per-Gunnar Martinsson, Vladimir Rokhlin, Mark Tygert
- Proceedings of the National Academy of Sciences…
- 2007

We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application (inter alia) to the evaluation of the singular… (More)

We introduce a randomized procedure that, given an m×n matrix A and a positive integer k, approximates A with a matrix Z of rank k. The algorithm relies on applying a structured l ×m random matrix R… (More)

- Nathan Halko, Per-Gunnar Martinsson, Yoel Shkolnisky, Mark Tygert
- SIAM J. Scientific Computing
- 2011

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy — even on parallel processors — unlike the classical… (More)

- Vladimir Rokhlin, Mark Tygert
- Proceedings of the National Academy of Sciences…
- 2008

We introduce a randomized algorithm for overdetermined linear least-squares regression. Given an arbitrary full-rank m x n matrix A with m >/= n, any m x 1 vector b, and any positive real number… (More)

Article history: Received 9 April 2008 Revised 23 August 2009 Accepted 13 February 2010 Available online 19 February 2010 Communicated by Charles K. Chui

- Vladimir Rokhlin, Mark Tygert
- SIAM J. Scientific Computing
- 2004

An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S2 in R3 of functions specified by their spherical harmonic expansions (known as the… (More)

Given an m × n matrix A and a positive integer k, we introduce a randomized procedure for the approximation of A with a matrix Z of rank k. The procedure relies on applying AT to a collection of l… (More)

- Mark Tygert
- J. Comput. Physics
- 2008

We provide an efficient algorithm for calculating, at appropriately chosen points on the two-dimensional surface of the unit sphere in R, the values of functions that are specified by their spherical… (More)

- Vladimir Rokhlin, Mark Tygert
- SIAM J. Scientific Computing
- 2011

We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the… (More)