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Rectangular matrix multiplication revisited. (English) Zbl 0872.68052
Summary: We give a constant \(\alpha> 0.294\) and, for any \(\varepsilon >0\), an algorithm for multiplying an \(N\times N\) matrix by an \(N\times N^\alpha\) matrix with complexity \(O(N^{2+ \varepsilon})\).

MSC:
68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
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[1] Bini, D.; Capovani, M.; Lotti, G.; Romani, F., On2.7799, Inform. process. lett., 8, 98-108, (1979)
[2] Coppersmith, D., Rapid multiplication of rectangular matrices, SIAM J. comput., 11, 467-471, (Aug. 1982)
[3] Coppersmith, D.; Winograd, S., Matrix multiplication via arithmetic progressions, J. symbolic comput., 9, 251-280, (1990) · Zbl 0702.65046
[4] Pan, V.Ya., How to multiply matrices faster, Springer lecture notes in computer science, 179, (1984), Springer-Verlag New York/Berlin
[5] R. Salem, D. C. Spencer, On sets of integers which contain no three terms in arithmetical progression, Proc. Natl. Acad. Sci. USA, 28, 561, 563 · Zbl 0060.10301
[6] Strassen, V., Gaussian elimination is not optimal, Numer. math., 13, 354-356, (1969) · Zbl 0185.40101
[7] V. Strassen, Relative bilinear complexity and matrix multiplication · Zbl 0621.68026
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