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 …

A randomized Gram--Schmidt algorithm is developed for orthonormalization of high-
dimensional vectors or QR factorization. The proposed process can be less computationally …

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 article introduces randomized block Gram-Schmidt process (RBGS) for QR
decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm …

We propose a probabilistic way for reducing the cost of classical projection-based model
order reduction methods for parameter-dependent linear equations. A reduced order model …

Nonlinear model order reduction has opened the door to parameter optimization and
uncertainty quantification in complex physics problems governed by nonlinear equations. In …

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 …

Classical model order reduction (MOR) for parametric problems may become
computationally inefficient due to large sizes of the required projection bases, especially for …