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Pré-Publication, Document De Travail Année : 2020

On fast multiplication of a matrix by its transpose

Résumé

We present a non-commutative algorithm for the multiplication of a block-matrix by its transpose over C or any finite field using 5 recursive products. We use geometric considerations on the space of bilinear forms describing 2×2 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 space and time efficient schedules that enable us to provide fast practical implementations for higher-dimensional matrix products.
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Dates et 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)

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Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic. On fast multiplication of a matrix by its transpose. 2020. ⟨hal-02432390v1⟩
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