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research article

A Parallel QZ Algorithm For Distributed Memory HPC Systems

Adlerborn, Bjoern
•
Kagstroem, Bo
•
Kressner, Daniel  
2014
SIAM Journal On Scientific Computing

Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm of Moler and Stewart is the most widely used algorithm for addressing such problems. Despite its importance, little attention has been paid to the parallelization of the QZ algorithm. The purpose of this work is to fill this gap. We propose a parallelization of the QZ algorithm that incorporates all modern ingredients of dense eigensolvers, such as multishift and aggressive early deflation techniques. To deal with (possibly many) infinite eigenvalues, a new parallel deflation strategy is developed. Numerical experiments for several random and application examples demonstrate the effectiveness of our algorithm on two different distributed memory HPC systems.

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Type
research article
DOI
10.1137/140954817
Web of Science ID

WOS:000346123200025

Author(s)
Adlerborn, Bjoern
Kagstroem, Bo
Kressner, Daniel  
Date Issued

2014

Publisher

Siam Publications

Published in
SIAM Journal On Scientific Computing
Volume

36

Issue

5

Start page

C480

End page

C503

Subjects

generalized eigenvalue problem

•

nonsymmetric QZ algorithm

•

multishift

•

bulge chasing

•

infinite eigenvalues

•

parallel algorithms

•

level 3 performance

•

aggressive early deflation

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
ANCHP  
Available on Infoscience
February 20, 2015
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/111201
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