Implementation of Strassen's Algorithm for Matrix Multiplication

In this paper we report on the development of an efficient and portable implementation of Strassen's matrix mulitplication algorithm. Our implementation is designed to be used in place of DGEMM, the Level 3 BLAS matrix mulitplication routine. Efficient performance will be obtained for all matrix sizes and shapes and the additional memory needed fro temporary variables has been minimized. Replacing DGEMM with our routine should provide a significant performance gain for large matrices while providing the same performance for small matrices. We measure performance of our code on the IBM RS/6000, CRAY YMP C90, and CRAY T3D single processor, and offer comparisons to other codes. Our performance data reconfirms that Strassen's algorithm is practical for realistic size matrices. The usefulness of our implementation is demonstrated by replacing DGEMM with our routine in a large application code.