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Multilevel communication optimal LU and QR factorizations for hierarchical platforms

Laura Grigori 1 Mathias Jacquelin 1 Amal Khabou 1
1 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
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 Hierarchical 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 analysis. We also provide a set of numerical experiments and performance predictions demonstrating the need for such algorithms on large platforms.
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Submitted on : Friday, March 22, 2013 - 4:08:01 PM
Last modification on : Friday, January 21, 2022 - 3:21:31 AM
Long-term archiving on: : Sunday, April 2, 2017 - 6:24:17 PM


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  • HAL Id : hal-00803718, version 1
  • ARXIV : 1303.5837


Laura Grigori, Mathias Jacquelin, Amal Khabou. Multilevel communication optimal LU and QR factorizations for hierarchical platforms. 2013. ⟨hal-00803718⟩



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