A Tensor Product Formulation of Strassen's Matrix Multiplication Algorithm with Memory Reduction

Bharat Kumar, Chua-Huang Huang, Rodney W. Johnson, P. Sadayappan

Abstract: A programming methodology based on tensor products has been used for designing and implementing block recursive algorithms for parallel and vector multiprocessors. A previous tensor product formulation of Strassen's matrix multiplication algorithm requires working arrays of size O(7/sup n/) for multiplying 2/sup n/*2/sup n/ matrices. The authors present a modified tensor product formulation of Strassen's algorithm in which the size of working arrays can be reduced to O(4/sup n/). The modified formulation exhibits sufficient parallel and vector operations for efficient implementation. Performance results on the Cray Y-MP are presented.< >