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

This paper introduces the Nyström preconditioned conjugate gradient (PCG) algorithm for
solving a symmetric positive-definite linear system. The algorithm applies the randomized …

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 …

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

Double descent refers to the phase transition that is exhibited by the generalization error of
unregularized learning models when varying the ratio between the number of parameters …

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 …

Viewing neural network models in terms of their loss landscapes has a long history in the
statistical mechanics approach to learning, and in recent years it has received attention …

Sketch-and-project is a framework which unifies many known iterative methods for solving
linear systems and their variants, as well as further extensions to nonlinear optimization …

We give a stochastic optimization algorithm that solves a dense n× n real-valued linear
system Ax= b, returning x such that|| A x− b||≤ є|| b|| in time: Õ ((n 2+ nk ω− 1) log1/є), where …

Large-scale subspace clustering usually drops the requirements of the full similarity matrix
and Laplacian matrix but constructs the anchor affinity matrix and uses matrix approximation …