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SCHEDULE: NOV 15-20, 2015

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Performance of Random Sampling for Computing Low-Rank Approximations of a Dense Matrix on GPUs

SESSION: Sampling in Matrix Computations

EVENT TYPE: Papers

EVENT TAG(S): Algorithms, Accelerators, Scientific Computing, Analytics

TIME: 11:00AM - 11:30AM

SESSION CHAIR(S): Shuaiwen Leon Song

AUTHOR(S):Theo Mary, Ichitaro Yamazaki, Jakub Kurzak, Piotr Luszczek, Stanimire Tomov, Jack Dongarra

ROOM:18CD

ABSTRACT:

Low-rank matrix approximations play an important role
in a wide range of applications. To compute a low-rank
approximation of a dense matrix, a common approach uses
the QR factorization with column pivoting (QRCP).
While reliable and efficient, this deterministic approach requires
costly communication, which is becoming
increasingly expensive on modern computers. We use
an alternative approach based on random sampling,
which requires much less communication than QRCP.
In this paper, we compare the performance
of the random sampling with that of QRCP on the
NVIDIA Kepler GPU. Our performance results demonstrate
that the random sampling method can be up to 13 times faster
compared to QRCP while computing
an approximation of comparable accuracy. We also present the
parallel scaling of random sampling over multiple GPUs,
showing a speedup of 5.1 over three GPUs.
These results demonstrate the potential of the random sampling as
an excellent computational tool for many applications.

Chair/Author Details:

Shuaiwen Leon Song (Chair) - Pacific Northwest National Laboratory|

Theo Mary - University of Toulouse

Ichitaro Yamazaki - University of Tennessee, Knoxville

Jakub Kurzak - University of Tennessee, Knoxville

Piotr Luszczek - University of Tennessee, Knoxville

Stanimire Tomov - University of Tennessee, Knoxville

Jack Dongarra - University of Tennessee, Knoxville

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Paper provided by the ACM Digital Library

Paper also available from IEEE Computer Society