Optimization techniques for small matrix multiplication

Authors:
Charles-Éric Drevet;Md. Nazrul Islam;Éric Schost
Affiliations:
Ancien élève, École polytechnique, Palaiseau, France;Department of Computer Science and ORCCA, The University of Western Ontario, London, ON, Canada;Department of Computer Science and ORCCA, The University of Western Ontario, London, ON, Canada
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

The complexity of matrix multiplication has attracted a lot of attention in the last forty years. In this paper, instead of considering asymptotic aspects of this problem, we are interested in reducing the cost of multiplication for matrices of small size, say up to 30. Following the previous work of Probert & Fischer, Smith, and Mezzarobba, in a similar vein, we base our approach on the previous algorithms for small matrices, due to Strassen, Winograd, Pan, Laderman, and others and show how to exploit these standard algorithms in an improved way. We illustrate the use of our results by generating multiplication codes over various rings, such as integers, polynomials, differential operators and linear recurrence operators.