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 …

We give a classical analogue to Kerenidis and Prakash's quantum recommendation system,
previously believed to be one of the strongest candidates for provably exponential speedups …

We design a new distribution over m× n matrices S so that, for any fixed n× d matrix A of rank
r, with probability at least 9/10,∥ SAx∥ 2=(1±ε)∥ Ax∥ 2 simultaneously for all x∈ R d …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

We develop and analyze a method to reduce the size of a very large set of data points in a
high-dimensional Euclidean space R^d to a small set of weighted points such that the result …

Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson,
and Tropp, randomized Simultaneous Power Iteration has become the method of choice for …

Several results appeared that show significant reduction in time for matrix multiplication,
singular value decomposition as well as linear (lscr 2) regression, all based on data …

Many data analysis applications deal with large matrices and involve approximating the
matrix using a small number of “components.” Typically, these components are linear …

A sketch of a matrix A is another matrix B which is significantly smaller than A but still
approximates it well. Finding such sketches efficiently is an important building block in …