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Conference Papers Year : 2020

On fast multiplication of a matrix by its transpose


We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field. We use geometric considerations on the space of bilinear forms describing 2x2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions. The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions. Finally we propose schedules with low memory footprint that support a fast and memory efficient practical implementation over a finite field. To conclude, we show how to use our result in LDLT factorization.
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Dates and versions

hal-02432390 , version 1 (08-01-2020)
hal-02432390 , version 2 (06-02-2020)
hal-02432390 , version 3 (04-05-2020)
hal-02432390 , version 4 (09-06-2020)



Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic. On fast multiplication of a matrix by its transpose. Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ACM SIGSAM, Jul 2020, Kalamata, Greece. pp.162-169, ⟨10.1145/3373207.3404021⟩. ⟨hal-02432390v4⟩
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