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A fast non-commutative algorithm for matrix multiplication

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Mathematical Foundations of Computer Science 1977 (MFCS 1977)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 53))

Abstract

In the paper a non-commutative algorithm for the multiplication of two square matrices of order n is presented. The algorithm requires n3-(n-1)2 multiplications and n3-n2+ 11 (n-1)2 additions. The recursive application of the algorithm for matrices of order nk leads to \(O(_n ^{k\log _n [n^3 - (n - 1)^2 ]} )\)operations to be executed.It is shown that some well-known algorithms are special cases of our algorithm. Finally, an improvement of the algorithm is given for matrices of order 5.

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References

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Authors and Affiliations

  1. Institute of Technical Cybernetics, Slovak Academy of Sciences, Dúbravská cesta 3, 809 31, Bratislava, Czechoslovakia

    Ondrej Sýkora

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  1. Ondrej Sýkora
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Jozef Gruska

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© 1977 Springer-Verlag Berlin Heidelberg

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Sýkora, O. (1977). A fast non-commutative algorithm for matrix multiplication. In: Gruska, J. (eds) Mathematical Foundations of Computer Science 1977. MFCS 1977. Lecture Notes in Computer Science, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08353-7_173

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  • DOI: https://doi.org/10.1007/3-540-08353-7_173

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08353-5

  • Online ISBN: 978-3-540-37285-1

  • eBook Packages: Springer Book Archive

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