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2013.11: Performance predictions of multilevel communication optimal LU and QR factorizations on hierarchical platforms

2013.11: Laura Grigori, Mathias Jacquelin and Amal Khabou (2013) Performance predictions of multilevel communication optimal LU and QR factorizations on hierarchical platforms.

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Abstract

In this paper we study the performance of two classical dense linear algebra algorithms, the LU and the QR factorizations, on multi- level hierarchical platforms. We note that we focus on multilevel QR factorization, and give a brief description of the multilevel LU factoriza- tion. We first introduce a performance model called Hierarchical Cluster Platform (HCP), encapsulating the characteristics of such platforms. The focus is set on reducing the communication requirements of studied al- gorithms at each level of the hierarchy. Lower bounds on communication are therefore extended with respect to the Hcp model. We then present a multilevel QR factorization algorithm tailored for those platforms, and provide a detailed performance analysis. We also provide a set of perfor- mance predictions showing the need for such hierarchical algorithms on large platforms.

Item Type:MIMS Preprint
Additional Information:

accepted in the International Supercomputing Conference (ISC14), and will be published in the Springer's Lecture Notes in Computer Science (LNCS) series.

Uncontrolled Keywords:QR, LU, exascale, hierarchical platforms
Subjects:MSC 2000 > 65 Numerical analysis
MIMS number:2013.11
Deposited By:Amal Khabou
Deposited On:08 April 2014

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