Parallel matrix multiplication is one of the most studied fundamental problems in distributed
and high performance computing. We obtain a new parallel algorithm that is based on …

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 …

Strassen's algorithm (1969) was the first sub-cubic matrix multiplication algorithm. Winograd
(1971) improved the leading coefficient of its complexity from 6 to 7. There have been many …

Matrix multiplication is one of the most extensively used kernels in scientific computing.
Although subcubic algorithms exist, most high performance implementations are based on …

In this paper, a new methodology for speeding up Matrix–Matrix Multiplication using Single
Instruction Multiple Data unit, at one and more cores having a shared cache, is presented …

Direct methods for the solution of sparse systems of linear equations are used in a wide
range of numerical simulation applications. Such methods are based on the decomposition …

Current compilers cannot generate code that can compete with hand-tuned code in
efficiency, even for a simple kernel like matrix–matrix multiplication (MMM). A key step in …

This article presents a new fast, highly scalable distributed matrix multiplication algorithm on
Apache Spark, called Stark, based on Strassen's matrix multiplication algorithm. Stark …

Alternative basis matrix multiplication algorithms are the fastest matrix multiplication
algorithms in practice to date. However, are they numerically stable? We obtain the first …

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