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DTSTAMP:20210808T235336Z
LOCATION:Room A
DTSTART;TZID=America/Chicago:20210811T121500
DTEND;TZID=America/Chicago:20210811T123000
UID:icpp_ICPP 2021_sess124_pap447@linklings.com
SUMMARY:Efficiently Parallelizable Strassen-Based Multiplication of a Matr
ix by its Transpose
DESCRIPTION:Conference Paper\n\nEfficiently Parallelizable Strassen-Based
Multiplication of a Matrix by its Transpose\n\nArrigoni, Maggioli, Massini
, RodolĂ \n\nThe multiplication of a matrix by its transpose, A^TA, appears
as an intermediate operation in the solution of a wide set of problems.\n
In this paper, we propose a new cache-oblivious algorithm (ATA) for comput
ing this product, based upon the classical Strassen algorithm as a sub-rou
tine. In particular, we decrease the computational cost to 2/3 the time re
quired by Strassen's algorithm, amounting to 14/3n^log_2 7 floating point
operations. ATA works for generic rectangular matrices, and exploits the p
eculiar symmetry of the resulting product matrix for saving memory. In add
ition, we provide an extensive implementation study of ATA in a shared mem
ory system, and extend its applicability to a distributed environment.\nTo
support our findings, we compare our algorithm with state-of-the-art solu
tions specialized in the computation of A^T*A, as well as with solutions f
or the computation of the general A^T*B product applied to this problem. O
ur experiments highlight good scalability with respect to both the matrix
size and the number of involved processes, as well as favorable performanc
e for both the parallel paradigms and the sequential implementation when c
ompared with other methods in the literature.
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