Abstract
Optimal use of either Strassen’s or Winograd’s algorithms for multiplying 2×2 matrices within the framework of Fischer and Probert yields only a relatively small reduction in Strassen’s constant of 4.7. Two additional schemes are discussed: minimal introduction of zero rows and columns, and permitting block multiplication as an additional tool. The first scheme yields extremely small improvement, but the second turns out to be highly effective.
This research was partially supported by the National Research Council of Canada, grant A-5549.
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Bibliography
Fischer, P.C., Probert, R.L., Efficient Procedures for Using Matrix Algorithms, these Proceedings (1974).
Strassen, V., Gaussian Elimination is not Optimal, Numer. Math. 13 (1969), 354–356.
Winograd, S., Private communication.
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© 1974 Springer-Verlag Berlin Heidelberg
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Fischer, P.C. (1974). Further Schemes for Combining Matrix Algorithms. In: Loeckx, J. (eds) Automata, Languages and Programming. ICALP 1974. Lecture Notes in Computer Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21545-6_32
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DOI: https://doi.org/10.1007/978-3-662-21545-6_32
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