#### Filter Results:

- Full text PDF available (35)

#### Publication Year

1998

2017

- This year (0)
- Last 5 years (23)
- Last 10 years (35)

#### Publication Type

#### Co-author

#### Journals and Conferences

Learn More

- Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp
- SIAM Review
- 2011

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This workâ€¦ (More)

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This workâ€¦ (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 â€” even on parallel processors â€” unlike the classicalâ€¦ (More)

- Edo Liberty, Franco Woolfe, Per-Gunnar Martinsson, V. Rokhlin, Mark Tygert
- Proceedings of the National Academy of Sciencesâ€¦
- 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 singularâ€¦ (More)

We describe an algorithm for the direct solution of systems of linear algebraic equations associated with the discretization of boundary integral equations with non-oscillatory kernels in twoâ€¦ (More)

- Per-Gunnar Martinsson
- SIAM J. Matrix Analysis Applications
- 2011

Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of suchâ€¦ (More)

An algorithm for the direct inversion of the linear systems arising from NystrÃ¶m discretization of integral equations on one-dimensional domains is described. The method typically has O(N) complexityâ€¦ (More)

- Hongwei Cheng, Zydrunas Gimbutas, Per-Gunnar Martinsson, Vladimir Rokhlin
- SIAM J. Scientific Computing
- 2005

A procedure is reported for the compression of rank-deficient matrices. A matrix A of rank k is represented in the form A = U â—¦B â—¦V , where B is a kÃ— k submatrix of A, and U , V are well-conditionedâ€¦ (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

Given an m Ã— 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 lâ€¦ (More)