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

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

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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 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Amal Khabou
Date Deposited: 08 Apr 2014
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2122

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