A scalable randomized least squares solver for dense overdetermined systems

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

doi:10.1145/2832080.2832083

A scalable randomized least squares solver for dense overdetermined systems

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

School of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We present a fast randomized least-squares solver for distributedmemory platforms. Our solver is based on the Blendenpik algorithm, but employs a batchwise randomized unitary transformation scheme. The batchwise transformation enables our algorithm to scale the distributed memory vanilla implementation of Blendenpik by up to×3 and provides up to×7.5 speedup over a state-of-the-art scalable least-squares solver based on the classic QR based algorithm. Experimental evaluations on terabyte scale matrices demonstrate excellent speedups on up to 16384 cores on a Blue Gene/Q supercomputer.

Original language	English
Title of host publication	Proceedings of ScalA 2015
Subtitle of host publication	6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis
Publisher	Association for Computing Machinery, Inc
ISBN (Electronic)	9781450340113
DOIs	https://doi.org/10.1145/2832080.2832083
State	Published - 15 Nov 2015
Event	6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2015 - Austin, United States Duration: 15 Nov 2015 → 20 Nov 2015

Publication series

Name	Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis

Conference

Conference	6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2015
Country/Territory	United States
City	Austin
Period	15/11/15 → 20/11/15

Funding

Funders	Funder number
IBM T.J. Watson Research Center
NSF IIS	IIS- 1302231
Defense Advanced Research Projects Agency
Air Force Research Laboratory	FA8750-12-C-0323
Air Force Research Laboratory

Keywords

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

Access to Document

10.1145/2832080.2832083

Cite this

Iyer, C., Avron, H., Kollias, G., Ineichen, Y., Carothers, C., & Drineas, P. (2015). A scalable randomized least squares solver for dense overdetermined systems. In Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis Article 3 (Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis). Association for Computing Machinery, Inc. https://doi.org/10.1145/2832080.2832083

Iyer, Chander ; Avron, Haim ; Kollias, Georgios et al. / A scalable randomized least squares solver for dense overdetermined systems. Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis. Association for Computing Machinery, Inc, 2015. (Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis).

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abstract = "We present a fast randomized least-squares solver for distributedmemory platforms. Our solver is based on the Blendenpik algorithm, but employs a batchwise randomized unitary transformation scheme. The batchwise transformation enables our algorithm to scale the distributed memory vanilla implementation of Blendenpik by up to×3 and provides up to×7.5 speedup over a state-of-the-art scalable least-squares solver based on the classic QR based algorithm. Experimental evaluations on terabyte scale matrices demonstrate excellent speedups on up to 16384 cores on a Blue Gene/Q supercomputer.",

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author = "Chander Iyer and Haim Avron and Georgios Kollias and Yves Ineichen and Christopher Carothers and Petros Drineas",

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Iyer, C, Avron, H, Kollias, G, Ineichen, Y, Carothers, C & Drineas, P 2015, A scalable randomized least squares solver for dense overdetermined systems. in Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis., 3, Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis, Association for Computing Machinery, Inc, 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2015, Austin, United States, 15/11/15. https://doi.org/10.1145/2832080.2832083

A scalable randomized least squares solver for dense overdetermined systems. / Iyer, Chander; Avron, Haim; Kollias, Georgios et al.
Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis. Association for Computing Machinery, Inc, 2015. 3 (Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Iyer C, Avron H, Kollias G, Ineichen Y, Carothers C, Drineas P. A scalable randomized least squares solver for dense overdetermined systems. In Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis. Association for Computing Machinery, Inc. 2015. 3. (Proceedings of ScalA 2015: 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis). doi: 10.1145/2832080.2832083

A scalable randomized least squares solver for dense overdetermined systems

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