Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic
structure theory and many other areas of computational science. The computational effort …

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 …

The computation of the singular value decomposition, or SVD, has a long history with many
improvements over the years, both in its implementations and algorithmically. Here, we …

The symmetric eigenvalue decomposition and the singular value decomposition (SVD) are
fundamental matrix decompositions with many applications. Conventional algorithms for …

Determinantal point processes (DPPs) were introduced by Macchi (Macchi 1975 Adv. Appl.
Probab. 7, 83–122) as a model for repulsive (fermionic) particle distributions. But their recent …

Many large-scale scientific computations require eigenvalue solvers in a scaling regime
where efficiency is limited by data movement. We introduce a parallel algorithm for …

Dense linear algebra computations are essential to nearly every problem in scientific
computing and to countless other fields. Most matrix computations enjoy a high …

We describe a design and implementation of a multi-stage algorithm for computing
eigenvectors of a dense symmetric matrix. We show that reformulating the existing …

In this work we revisit the arithmetic and bit complexity of Hermitian eigenproblems. We first
provide an analysis for the divide-and-conquer tridiagonal eigensolver of Gu and Eisenstat …

The convergence of several unprecedented changes, including formidable new system
design constraints and revolutionary levels of heterogeneity, has made it clear that much of …