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Scientific Programming
Volume 4 (1995), Issue 4, Pages 275-289

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

B. Kumar,1 C.-H. Huang,1 P. Sadayappan,1 and R.W. Johnson2

1Department of Computer and Information Science, The Ohio State University, Columbus, OH 43210-1277, USA
2Department of Computer Science, St. Cloud State University, St. Cloud, MN 56301, USA

Received 17 September 1994; Accepted 17 April 1995

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this article, we present a program generation strategy of Strassen's matrix multiplication algorithm using a programming methodology based on tensor product formulas. In this methodology, block recursive programs such as the fast Fourier Transforms and Strassen's matrix multiplication algorithm are expressed as algebraic formulas involving tensor products and other matrix operations. Such formulas can be systematically translated to high-performance parallel/vector codes for various architectures. In this article, we present a nonrecursive implementation of Strassen's algorithm for shared memory vector processors such as the Cray Y-MP. A previous implementation of Strassen's algorithm synthesized from tensor product formulas required working storage of size O(7n) for multiplying 2n × 2n matrices. We present a modified formulation in which the working storage requirement is reduced to O(4n). The modified formulation exhibits sufficient parallelism for efficient implementation on a shared memory multiprocessor. Performance results on a Cray Y-MP8/64 are presented.