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Matrix multiplication is a fundamental kernel of many high performance and scientific computing applications. Most parallel implementations use classical O(n3) matrix multiplication, even though there exist algorithms with lower arithmetic complexity. We recently presented a new Communication-Avoiding Parallel Strassen algorithm (CAPS), based on Strassen's fast matrix multiplication, that minimizes communication (SPAA'12). It communicates asymptotically less than all classical and all previous Strassen-based algorithms, and it attains theoretical lower bounds. In this paper we show that CAPS is also faster in practice. We benchmark and compare its performance to previous algorithms on Hopper (Cray XE6), Intrepid (IBM BG/P), and Franklin (Cray XT4). We demonstrate significant speedups over previous algorithms both for large matrices and for small matrices on large numbers of processors. We model and analyze the performance of CAPS and predict its performance on future exascale platforms. [ABSTRACT FROM PUBLISHER]

We present CARMA, the first implementation of a communication-avoiding parallel rectangular matrix multiplication algorithm, attaining significant speedups over both MKL and ScaLAPACK. Combining the recursive BFS/DFS approach of Ballard, Demmel, Holtz, Lipshitz and Schwartz (SPAA '12) with the dimension splitting technique of Frigo, Leiserson, Prokop and Ramachandron (FOCS '99), CARMA is communication-optimal, cache- and network-oblivious, and simple to implement (60 lines of code for the shared-memory version). Since CARMA minimizes communication across the network, between NUMA domains, and between levels of cache, it performs well on both shared- and distribute-memory machines. [ABSTRACT FROM PUBLISHER]