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

The computation of, the action of a matrix function on a vector, is a task arising in many
areas of scientific computing. In many applications, the matrix is sparse but so large that only …

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

This article proposes and analyzes several variants of the randomized Cholesky QR
factorization of a matrix $ X $. Instead of computing the R factor from $ X^ TX $, as is done by …

A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix
functions acting on a set of vectors is developed. The method improves over the recycling …

Thanks to its great potential in reducing both computational cost and memory requirements,
combining sketching and Krylov subspace techniques has attracted a lot of attention in the …

A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space
at low cost is proposed. At each iteration the procedure utilizes randomized sketching to …

Thanks to its great potential in reducing both computational cost and memory requirements,
combining sketching and Krylov subspace techniques has attracted a lot of attention in the …

With the recent realization of exascale performance by Oak Ridge National Laboratory's
Frontier supercomputer, reducing communication in kernels like QR factorization has …