Parallel Matrix Multiplication: A Systematic Journey
| Autor: | Jack Poulson, Robert A. van de Geijn, Martin D. Schatz |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Multiplication algorithm
Analysis of parallel algorithms Computer science Applied Mathematics 020206 networking & telecommunications 010103 numerical & computational mathematics 02 engineering and technology Parallel computing 01 natural sciences Matrix multiplication Computational Mathematics Parallel processing (DSP implementation) Scalability Linear algebra 0202 electrical engineering electronic engineering information engineering Polygon mesh Multiplication 0101 mathematics Algorithm |
| Zdroj: | SIAM Journal on Scientific Computing. 38:C748-C781 |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/140993478 |
| Popis: | We expose a systematic approach for developing distributed-memory parallel matrix-matrix multiplication algorithms. The journey starts with a description of how matrices are distributed to meshes of nodes (e.g., MPI processes), relates these distributions to scalable parallel implementation of matrix-vector multiplication and rank-1 update, continues on to reveal a family of matrix-matrix multiplication algorithms that view the nodes as a two-dimensional (2D) mesh, and finishes with extending these 2D algorithms to so-called three-dimensional (3D) algorithms that view the nodes as a 3D mesh. A cost analysis shows that the 3D algorithms can attain the (order of magnitude) lower bound for the cost of communication. The paper introduces a taxonomy for the resulting family of algorithms and explains how all algorithms have merit depending on parameters such as the sizes of the matrices and architecture parameters. The techniques described in this paper are at the heart of the Elemental distributed-memory line... |
| Databáze: | OpenAIRE |
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