Multilevel communication optimal LU and QR factorizations for hierarchical platforms

Grigori, Laura and Jacquelin, Mathias and Khabou, Amal (2013) Multilevel communication optimal LU and QR factorizations for hierarchical platforms. [MIMS Preprint]

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Abstract

This study focuses on the performance of two classical dense linear algebra algorithms, the LU and the QR factorizations, on multilevel hierarchical platforms. We first introduce a new model called Hi- erarchical Cluster Platform (HCP), encapsulating the characteristics of such platforms. The focus is set on reducing the communication requirements of studied algorithms at each level of the hierarchy. Lower bounds on communications are therefore extended with respect to the HCP model. We then introduce multilevel LU and QR algorithms tailored for those platforms, and provide a detailed performance anal- ysis. We also provide a set of numerical experiments and performance predictions demonstrating the need for such algorithms on large platforms.

Item Type: MIMS Preprint
Additional Information: submitted to the 25th ACM Symposium on Parallelism in Algorithms and Architectures
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: 13 Mar 2013
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1959

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