Matrix powers kernels for thick-restart Lanczos with explicit external deflation

Zhaojun Bai, Jack Dongarra, Ding Lu, Ichitaro Yamazaki

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Some scientific and engineering applications need to compute a large number of eigenpairs of a large Hermitian matrix. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenpairs (e.g., in terms of computation and communication). To improve the performance of the method, in this paper, we study an s-step variant of thick-restart Lanczos (TRLan) combined with an explicit external deflation (EED). The s-step method generates a set of s basis vectors at a time and reduces the communication costs of generating the basis vectors. We then design a specialized matrix powers kernel (MPK) that reduces both the communication and computational costs by taking advantage of the special properties of the deflation matrix. We conducted numerical experiments of the new TRLan eigensolver using synthetic matrices and matrices from electronic structure calculations. The performance results on the Cori supercomputer at the National Energy Research Scientific Computing Center (NERSC) demonstrate the potential of the specialized MPK to significantly reduce the execution time of the TRLan eigensolver. The speedups of up to 3.1× and 5.3× were obtained in our sequential and parallel runs, respectively.

Original languageEnglish
Title of host publicationProceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019
Pages472-481
Number of pages10
ISBN (Electronic)9781728112466
DOIs
StatePublished - May 2019
Event33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019 - Rio de Janeiro, Brazil
Duration: May 20 2019May 24 2019

Publication series

NameProceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019

Conference

Conference33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019
Country/TerritoryBrazil
CityRio de Janeiro
Period5/20/195/24/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Information Systems and Management

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