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 …

Matrices are exceptionally useful in various fields of study as they provide a convenient
framework to organize and manipulate data in a structured manner. However, modern …

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 …

This paper develops a class of algorithms for general linear systems and eigenvalue
problems. These algorithms apply fast randomized dimension reduction (“sketching”) to …

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 …

Data-driven algorithms can adapt their internal structure or parameters to inputs from
unknown application-specific distributions, by learning from a training sample of inputs …

This survey explores modern approaches for computing low-rank approximations of high-
dimensional matrices by means of the randomized SVD, randomized subspace iteration …

With the increase in collected data volumes, either from experimental measurements or high
fidelity simulations, there is an ever-growing need to develop computationally efficient tools …