Structured Parallel Programming offers the simplest way for developers to learn patterns for
high-performance parallel programming. Written by parallel computing experts and industry …

We highlight the trends leading to the increased appeal of using hybrid multicore+ GPU
systems for high performance computing. We present a set of techniques that can be used to …

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 …

Extra memory allows parallel matrix multiplication to be done with asymptotically less
communication than Cannon's algorithm and be faster in practice.“3D” algorithms arrange …

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 the standard method for solving systems of linear equations, Gaussian elimination (GE) is
one of the most important and ubiquitous numerical algorithms. However, its successful use …

Gaussian elimination is a canonical linear algebra procedure for solving linear systems of
equations. In the last few years, the algorithm has received a lot of attention in an attempt to …

The communication cost of algorithms (also known as I/O-complexity) is shown to be closely
related to the expansion properties of the corresponding computation graphs. We …

In this paper we introduce CARRQR, a communication avoiding rank revealing QR
factorization with tournament pivoting. We show that CARRQR reveals the numerical rank of …

We present a new approach to utilizing all CPU cores and all GPUs on heterogeneous
multicore and multi-GPU systems to support dense matrix computations efficiently. The main …