Second-generation polyalgorithms for parallel dense-matrix multiplication

The polyalgorithm library, originally designed in 1991-1993 by Robert Falgout, Jin Li, and Anthony Skjellum, includes fourteen dense matrix multiplication algorithms mapped onto two-dimensional process grids using the Message Passing Interface (MPI). This thesis' goal is to achieve optimized performance of parallel, dense linear algebra algorithms by varying the algorithm as a function of problem size, shape, data layout, concurrency, and architecture. We integrate these algorithms with an intra-node BLAS DGEMM kernel designed by Thomas Hines (Tennessee Tech), which improves the BLAS DGEMM performance in fat-by-thin dense matrix multiplication region. We add a rank-k-based SUMMA algorithm, which performs better than rank-1-based SUMMA. We studied performance on two cluster systems and results show the performance and improvements achieved. We compare and contrast our results with COSMA, a recent, highly optimized approach, and verify that COSMA, using optimal 3D grid decompositions, has significant advantages provided its preferred data layouts can be used.

Grantor dc:publisher

University of Tennessee at Chattanooga

Author dc:creator

• Nansamba, Grace

Contributors dc:contributor

• Skjellum, Anthony
• Kandah, Farah; Ward, Michael
• College of Engineering and Computer Science

• Mathematical optimization
• Multiplication, Complex

Licence

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/680

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-1853