A New Direction to Parallelize Winograd’s Algorithm on Distributed Memory Computers

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Winograd’s algorithm to multiply two n × n matrices reduces the asymptotic operation count from O(n 3) of the traditional algorithm to O(n 2.81), hence on distributed memory computers, the combination of Winograd’s algorithm and the parallel matrix multiplication algorithms always gives remarkable results. Within this combination, the application of Winograd’s algorithm at the inter-processor level requires us to solve more difficult problems but it leads to more effective algorithms. In this paper, a general formulation of these algorithms will be presented. We also introduce a scalable method to implement these algorithms on distributed memory computers. This work also opens a new direction to parallelize Winograd’s algorithm based on the generalization of Winograd’s formula for the case where the matrices are partitioned into 2 k parts (the case k = 2 gives us the original formula).