Papers › Efficiently Parallelizable Strassen-Based Multiplication of a Matrix by its Transpose
Efficiently Parallelizable Strassen-Based Multiplication of a Matrix by its Transpose
Viviana Arrigoni, Filippo Maggioli, Annalisa Massini, Emanuele Rodolà
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The multiplication of a matrix by its transpose, Aᵀ A, appears as an intermediate operation in the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm (ATA) for computing this product, based upon the classical Strassen algorithm as a sub-routine. In particular, we decrease the computational cost to 2/3 the time required by Strassen's algorithm, amounting to 14/3n^(log₂ 7) floating point operations. ATA works for generic rectangular matrices, and exploits the peculiar symmetry of the resulting product matrix for saving memory. In addition, we provide an extensive implementation study of ATA in a shared memory system, and extend its applicability to a distributed environment. To support our findings, we compare our algorithm with state-of-the-art solutions specialized in the computation of Aᵀ A. Our experiments highlight good scalability with respect to both the matrix size and the number of involved processes, as well as favorable performance for both the parallel paradigms and the sequential implementation, when compared with other methods in the literature.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections