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 …

Low rank approximation of matrices has been well studied in literature. Singular value
decomposition, QR decomposition with column pivoting, rank revealing QR factorization …

This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

Our goal in this paper is to show that many of the tools of signal processing, adapted Fourier
and wavelet analysis can be naturally lifted to the setting of digital data clouds, graphs, and …

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 …

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

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 …

This article describes a fast direct solver (ie, not iterative) for partial hierarchically semi-
separable systems. This solver requires a storage of\mathcal O (N\log N) O (N log N) and …

A new O (N) fast multipole formulation is proposed for non-oscillatory kernels. This algorithm
is applicable to kernels K (x, y) which are only known numerically, that is their numerical …

In applications, a high-dimensional data is given as a discrete set in a Euclidean space. If
the points of data are well sampled on a manifold, then the data geometry is inherited from …