SUMMARY In 1907, Erhard Schmidt published a paper in which he introduced an
orthogonalization algorithm that has since become known as the classical Gram‐Schmidt …

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 …

Today's floating-point arithmetic landscape is broader than ever. While scientific computing
has traditionally used single precision and double precision floating-point arithmetics, half …

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 …

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

As much as Graph Convolutional Networks (GCNs) have shown tremendous success in
recommender systems and collaborative filtering (CF), the mechanism of how they …

Solvers for large sparse linear systems come in two categories: direct and iterative.
Amesos2, a package in the Trilinos software project, provides direct methods, and Belos …

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

Anasazi is a package within the Trilinos software project that provides a framework for the
iterative, numerical solution of large-scale eigenvalue problems. Anasazi is written in ANSI …

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 …