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A Framework for Out of Memory SVD Algorithms

  • Khairul Kabir
  • Azzam HaidarEmail author
  • Stanimire Tomov
  • Aurelien Bouteiller
  • Jack Dongarra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10266)

Abstract

Many important applications – from big data analytics to information retrieval, gene expression analysis, and numerical weather prediction – require the solution of large dense singular value decompositions (SVD). In many cases the problems are too large to fit into the computer’s main memory, and thus require specialized out-of-core algorithms that use disk storage. In this paper, we analyze the SVD communications, as related to hierarchical memories, and design a class of algorithms that minimizes them. This class includes out-of-core SVDs but can also be applied between other consecutive levels of the memory hierarchy, e.g., GPU SVD using the CPU memory for large problems. We call these out-of-memory (OOM) algorithms. To design OOM SVDs, we first study the communications for both classical one-stage blocked SVD and two-stage tiled SVD. We present the theoretical analysis and strategies to design, as well as implement, these communication avoiding OOM SVD algorithms. We show performance results for multicore architecture that illustrate our theoretical findings and match our performance models.

Keywords

Singular Value Decomposition Singular Vector Solid State Drive Tile Size Band Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Khairul Kabir
    • 4
  • Azzam Haidar
    • 1
    Email author
  • Stanimire Tomov
    • 1
  • Aurelien Bouteiller
    • 1
  • Jack Dongarra
    • 1
    • 2
    • 3
  1. 1.University of TennesseeKnoxvilleUSA
  2. 2.Oak Ridge National LaboratoryOak RidgeUSA
  3. 3.University of ManchesterManchesterUK
  4. 4.NvidiaSanta ClaraUSA

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