A Parallel QZ Algorithm for Distributed Memory HPC Systems

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 pa...

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Vydané v:SIAM journal on scientific computing Ročník 36; číslo 5; s. C480 - C503
Hlavní autori: Adlerborn, Björn, Kågström, Bo, Kressner, Daniel
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: 01.01.2014
Predmet:
1993
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
aggressive early deflation
Algorithms
bulge chasing
Computation
Distributed memory
Eigenvalues
generalized eigenvalue problem
infinite genvalues
Ingredients
level 3 performance
Linear algebra
MMEL J
multishift
nonsymmetric QZ algorithm
P175
parallel algorithms
Parallel processing
Strategy
V19
ISSN:1064-8275, 1095-7197, 1095-7197
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Abstract 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.
AbstractList 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.
Author Adlerborn, Björn
Kågström, Bo
Kressner, Daniel
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  surname: Kressner
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Snippet Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm of Moler...
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SubjectTerms 1993
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
aggressive early deflation
Algorithms
bulge chasing
Computation
Distributed memory
Eigenvalues
generalized eigenvalue problem
infinite genvalues
Ingredients
level 3 performance
Linear algebra
MMEL J
multishift
nonsymmetric QZ algorithm
P175
parallel algorithms
Parallel processing
Strategy
V19
Title A Parallel QZ Algorithm for Distributed Memory HPC Systems
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