A fast non-commutative algorithm for matrix multiplication

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


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.


Matrix Multiplication Arithmetical Operation Expression A23632 Recursive Application Require Scalar 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Ondrej Sýkora
    • 1
  1. 1.Institute of Technical CyberneticsSlovak Academy of SciencesBratislavaCzechoslovakia

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