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 …

Semidefinite programming (SDP) is a powerful framework from convex optimization that has
striking potential for data science applications. This paper develops a provably correct …

Kernel k-means clustering can correctly identify and extract a far more varied collection of
cluster structures than the linear k-means clustering algorithm. However, kernel k-means …

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 argues that randomized linear sketching is a natural tool for on-the-fly
compression of data matrices that arise from large-scale scientific simulations and data …

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

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

The implicit trace estimation problem asks for an approximation of the trace of a square
matrix, accessed via matrix-vector products (matvecs). This paper designs new randomized …

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 …