A randomized least squares solver for terabyte-sized dense overdetermined systems

Chander Iyer; Haim Avron; Georgios Kollias; Yves Ineichen; Christopher Carothers; Petros Drineas

doi:10.1016/j.jocs.2016.09.007

A randomized least squares solver for terabyte-sized dense overdetermined systems

Chander Iyer^*, Haim Avron, Georgios Kollias, Yves Ineichen, Christopher Carothers, Petros Drineas

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We present a fast randomized least-squares solver for distributed-memory platforms. Our solver is based on the Blendenpik algorithm, but employs multiple random projection schemes to construct a sketch of the input matrix. These random projection sketching schemes, and in particular the use of the randomized Discrete Cosine Transform, enable our algorithm to scale the distributed memory vanilla implementation of Blendenpik to terabyte-sized matrices and provide up to ×7.5 speedup over a state-of-the-art scalable least-squares solver based on the classic QR algorithm. Experimental evaluations on terabyte scale matrices demonstrate excellent speedups on up to 16,384 cores on a Blue Gene/Q supercomputer.

Original language	English
Article number	100547
Journal	Journal of Computational Science
Volume	36
DOIs	https://doi.org/10.1016/j.jocs.2016.09.007
State	Published - Sep 2019

Funding

Funders	Funder number
National Science Foundation	IIS-1302231
U.S. Department of Energy
Defense Advanced Research Projects Agency
International Business Machines Corporation
AT and T
Air Force Research Laboratory	FA8750- 12-C-0323
Army Research Laboratory

Keywords

Dense least squares regression
High-performance computing
Randomized numerical linear algebra

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10.1016/j.jocs.2016.09.007

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abstract = "We present a fast randomized least-squares solver for distributed-memory platforms. Our solver is based on the Blendenpik algorithm, but employs multiple random projection schemes to construct a sketch of the input matrix. These random projection sketching schemes, and in particular the use of the randomized Discrete Cosine Transform, enable our algorithm to scale the distributed memory vanilla implementation of Blendenpik to terabyte-sized matrices and provide up to ×7.5 speedup over a state-of-the-art scalable least-squares solver based on the classic QR algorithm. Experimental evaluations on terabyte scale matrices demonstrate excellent speedups on up to 16,384 cores on a Blue Gene/Q supercomputer.",

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AU - Iyer, Chander

AU - Avron, Haim

AU - Kollias, Georgios

AU - Ineichen, Yves

AU - Carothers, Christopher

AU - Drineas, Petros

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AB - We present a fast randomized least-squares solver for distributed-memory platforms. Our solver is based on the Blendenpik algorithm, but employs multiple random projection schemes to construct a sketch of the input matrix. These random projection sketching schemes, and in particular the use of the randomized Discrete Cosine Transform, enable our algorithm to scale the distributed memory vanilla implementation of Blendenpik to terabyte-sized matrices and provide up to ×7.5 speedup over a state-of-the-art scalable least-squares solver based on the classic QR algorithm. Experimental evaluations on terabyte scale matrices demonstrate excellent speedups on up to 16,384 cores on a Blue Gene/Q supercomputer.

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A randomized least squares solver for terabyte-sized dense overdetermined systems

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