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

In: Modeling, Simulation and Optimization of Complex Processes

Author

Listed:
  • D. K. Nguyen

    (CHArt - Ecole Pratique des Hautes Etudes & Université Paris 8)

  • I. Lavallee

    (LaISC - Ecole Pratique des Hautes Etudes)

  • M. Bui

    (LaISC - Ecole Pratique des Hautes Etudes)

Abstract

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).

Suggested Citation

  • D. K. Nguyen & I. Lavallee & M. Bui, 2008. "A New Direction to Parallelize Winograd’s Algorithm on Distributed Memory Computers," Springer Books, in: Hans Georg Bock & Ekaterina Kostina & Hoang Xuan Phu & Rolf Rannacher (ed.), Modeling, Simulation and Optimization of Complex Processes, pages 445-457, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-79409-7_31
    DOI: 10.1007/978-3-540-79409-7_31
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