Abstract | ||
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We present a non-commutative algorithm for the multiplication of a 2 × 2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any field of prime characteristic. 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 schedules with low memory footprint that support a fast and memory efficient practical implementation over a prime field. To conclude, we show how to use our result in L · D · LT factorization.
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Year | DOI | Venue |
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2020 | 10.1145/3373207.3404021 | ISSAC '20: International Symposium on Symbolic and Algebraic Computation
Kalamata
Greece
July, 2020 |
DocType | ISBN | Citations |
Conference | 978-1-4503-7100-1 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
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Jean-Guillaume Dumas | 1 | 428 | 68.48 |
Clément Pernet | 2 | 243 | 39.00 |
Sedoglavic Alexandre | 3 | 0 | 0.34 |