The randomly pivoted Cholesky algorithm (RPCholesky) computes a factorized rank‐kk
approximation of an N× NN*N positive‐semidefinite (psd) matrix. RPCholesky requires only …

Randomized SVD has become an extremely successful approach for efficiently computing a
low-rank approximation of matrices. In particular the paper by Halko, Martinsson, and Tropp …

We study the Kronecker product regression problem, in which the design matrix is a
Kronecker product of two or more matrices. Formally, given $ A_i\in\R^{n_i\times d_i} $ for …

Leverage score sampling is a powerful technique that originates from theoretical computer
science, which can be used to speed up a large number of fundamental questions, eg linear …

Several important applications, such as streaming PCA and semidefinite programming,
involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of …

We study iterative methods based on Krylov subspaces for low-rank approximation under
any Schatten-p norm. Here, given access to a matrix A through matrix-vector products, an …

We create classical (non-quantum) dynamic data structures supporting queries for
recommender systems and least-squares regression that are comparable to their quantum …

We consider the problem of rank-1 low-rank approximation (LRA) in the matrix-vector
product model under various Schatten norms: _ ‖ u ‖ _ 2= 1\left ‖ A\left (Iu u …

Large matrices arise in many machine learning and data analysis applications, including as
representations of datasets, graphs, model weights, and first and second-order derivatives …

Inspired by fast algorithms in natural language processing, we study low rank approximation
in the entrywise transformed setting where we want to find a good rank $ k $ approximation …