The traditional metric for the efficiency of a numerical algorithm has been the number of
arithmetic operations it performs. Technological trends have long been reducing the time to …

Irregular applications such as big graph analysis, material simulations, molecular dynamics
simulations, and finite element analysis have performance problems due to their use of …

We present parallel and sequential dense QR factorization algorithms that are both optimal
(up to polylogarithmic factors) in the amount of communication they perform and just as …

Graph Neural Networks (GNNs) are powerful and flexible neural networks that use the
naturally sparse connectivity information of the data. GNNs represent this connectivity as …

Krylov subspace methods (KSMs) are iterative algorithms for solving large, sparse linear
systems and eigenvalue problems. Current KSMs rely on sparse matrix-vector multiply …

This work revisits existing algorithms for the QR factorization of rectangular matrices
composed of p× q tiles, where p≥ q. Within this framework, we study the critical paths and …

Advancements in the field of high-performance scientific computing are necessary to
address the most important challenges we face in the 21st century. From physical modeling …

We describe an implementation of the Communication-Avoiding QR (CAQR) factorization
that runs entirely on a single graphics processor (GPU). We show that the reduction in …

We present efficient and scalable parallel algorithms for performing mathematical operations
for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for …

The Cholesky QR algorithm is an efficient communication-minimizing algorithm for
computing the QR factorization of a tall-skinny matrix X∈R^m*n, where m≫n. Unfortunately …