Randomized numerical linear algebra-RandNLA, for short-concerns the use of
randomization as a resource to develop improved algorithms for large-scale linear algebra …

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 …

We reconsider randomized algorithms for the low-rank approximation of symmetric positive
semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data …

This paper describes a suite of algorithms for constructing low-rank approximations of an
input matrix from a random linear image, or sketch, of the matrix. These methods can …

The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares
problems. At each step, the algorithm projects the current iterate onto the solution space of a …

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The
method is based on an approximate series expansion of the covariance function in terms of …

Kernel ridge regression (KRR) is a standard method for performing nonparametric
regression over reproducing kernel Hilbert spaces. Given n samples, the time and space …

The CUR decomposition of an m× n matrix A finds an m× c matrix C with a small subset of c<
n columns of A, together with an r× n matrix R with a small subset of r< m rows of A, as well …

Matrix skeletonizations like the interpolative and CUR decompositions provide a framework
for low-rank approximation in which subsets of a given matrix's columns and/or rows are …

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a
tensor. The method applies a randomized linear map to the tensor to obtain a sketch that …