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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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|
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|
|Deposited By:||Amal Khabou|
|Deposited On:||08 April 2014|
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