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Anatomy of high-performance matrix multiplication
We present the basic principles that underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. Design decisions are justified…
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SUMMA: scalable universal matrix multiplication algorithm
In this paper, we give a straight forward, highly efficient, scalable implementation of common matrix multiplication operations. The algorithms are much simpler than previously published methods,…
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BLIS: A Framework for Rapidly Instantiating BLAS Functionality
TLDR
Preliminary performance of level-2 and level-3 operations is observed to be competitive with two mature open source libraries (OpenBLAS and ATLAS) as well as an established commercial product (Intel MKL).
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High-performance implementation of the level-3 BLAS
A simple but highly effective approach for transforming high-performance implementations on cache-based architectures of matrix-matrix multiplication into implementations of other commonly used…
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Elemental: A New Framework for Distributed Memory Dense Matrix Computations
TLDR
Preliminary performance results show the new solution achieves competitive, if not superior, performance on large clusters, and a simple yet effective alternative to the traditional MPI-based approaches.
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Collective communication: theory, practice, and experience
TLDR
This paper discusses the design and high‐performance implementation of collective communications operations on distributed‐memory computer architectures and develops implementations that have improved performance in most situations compared to those currently supported by public domain implementations of MPI.
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Using PLAPACK - parallel linear algebra package
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Parallel Solution of Integral Equation-Based EM Problems in the Frequency Domain
TLDR
This textbook contains 64 algorithms for finding sparse solutions of underdetermined linear systems and their applications for matrix completion, graph clustering, and phase retrieval and provides a detailed explanation of these algorithms including derivations and convergence analysis.
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SuperMatrix: a multithreaded runtime scheduling system for algorithms-by-blocks
This paper describes SuperMatrix, a runtime system that parallelizes matrix operations for SMP and/or multi-core architectures. We use this system to demonstrate how code described at a high level of…
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Supermatrix out-of-order scheduling of matrix operations for SMP and multi-core architectures
TLDR
It is argued that traditional implementations of dense linear algebra matrix operations on SMP architectures cannot be easily modified to render high performance as well as scalability on these architectures, and the solution is to arrange the data structures and algorithms so that matrix blocks become the fundamental units of data.
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