Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
LAPACK's user's guide
ScaLAPACK user's guide
A cellular computer to implement the kalman filter algorithm
A cellular computer to implement the kalman filter algorithm
MapReduce: simplified data processing on large clusters
OSDI'04 Proceedings of the 6th conference on Symposium on Opearting Systems Design & Implementation - Volume 6
Evaluating MapReduce for Multi-core and Multiprocessor Systems
HPCA '07 Proceedings of the 2007 IEEE 13th International Symposium on High Performance Computer Architecture
Scheduling dense linear algebra operations on multicore processors
Concurrency and Computation: Practice & Experience
Phoenix rebirth: Scalable MapReduce on a large-scale shared-memory system
IISWC '09 Proceedings of the 2009 IEEE International Symposium on Workload Characterization (IISWC)
Optimizing OpenMP parallelized DGEMM calls on SGI altix 3700
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Parallelization of general matrix multiply routines using OpenMP
WOMPAT'04 Proceedings of the 5th international conference on OpenMP Applications and Tools: shared Memory Parallel Programming with OpenMP
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The current trend of multicore and Symmetric Multi-Processor (SMP), architectures underscores the need for parallelism in most scientific computations. Matrix-matrix multiplication is one of the fundamental computations in many algorithms for scientific and numerical analysis. Although a number of different algorithms (such as Cannon, PUMMA, SUMMA etc), have been proposed for the implementation of matrix-matrix multiplication on distributed memory architectures, matrix-matrix algorithms for multicore and SMP architectures have not been extensively studied. We present two types of algorithms, based largely on blocked dense matrices, for parallel matrix-matrix multiplication on shared memory systems. The first algorithm is based on blocked matrices whiles the second algorithm uses blocked matrices with the MapReduce framework in shared memory. Our experimental results show that, our blocked dense matrix approach outperforms the known existing implementations by up to 50% whiles our MapReduce blocked matrix-matrix algorithm outperforms the existing matrix-matrix multiplication algorithm of the Phoenix shared memory MapReduce approach, by about 40%.