Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

A novel parallel QR algorithm for hybrid distributed memory HPC systems

by R. Granat and B. Kagstroem and D. Kressner

(Report number 2009-15)

Abstract
A novel variant of the parallel QR algorithm for solving dense nonsymmetric eigenvalue problems on hybrid distributed high performance computing (HPC) systems is presented. For this purpose, we introduce the concept of multi-window bulge chain chasing and parallelize aggressive early deflation. The multi-window approach ensures that most computations when chasing chains of bulges are performed in level 3 BLAS operations, while the aim of aggressive early deflation is to speed up the convergence of the QR algorithm. Mixed MPI-OpenMP coding techniques are utilized for porting the codes to distributed memory platforms with multithreaded nodes, such as multicore processors. Numerous numerical experiments confirm the superior performance of our parallel QR algorithm in comparison with the existing ScaLAPACK code, leading to an implementation that is one to two orders of magnitude faster for sufficiently large problems, including a number of examples from applications.

Keywords: Eigenvalue problem, nonsymmetric QR algorithm, multishift, bulge chasing, parallel computations, level 3 performance, aggressive early deflation, parallel algorithms, hybrid distributed memory systems

@Techreport{GKK09_402,
  author = {R. Granat and B. Kagstroem and D. Kressner},
  title = {A novel parallel QR algorithm for hybrid distributed memory HPC systems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-15.pdf },
  year = {2009}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).