Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem

Handle URI:
http://hdl.handle.net/10754/555650
Title:
Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem
Authors:
Haidar, Azzam; Ltaief, Hatem ( 0000-0002-6897-1095 ) ; Dongarra, Jack
Abstract:
Classical solvers for the dense symmetric eigenvalue problem suffer from the first step, which involves a reduction to tridiagonal form that is dominated by the cost of accessing memory during the panel factorization. The solution is to reduce the matrix to a banded form, which then requires the eigenvalues of the banded matrix to be computed. The standard divide and conquer algorithm can be modified for this purpose. The paper combines this insight with tile algorithms that can be scheduled via a dynamic runtime system to multicore architectures. A detailed analysis of performance and accuracy is included. Performance improvements of 14-fold and 4-fold speedups are reported relative to LAPACK and Intel's Math Kernel Library.
KAUST Department:
KAUST Supercomputing Laboratory (KSL)
Citation:
Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem 2012, 34 (6):C249 SIAM Journal on Scientific Computing
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
Jan-2012
DOI:
10.1137/110823699
Type:
Article
ISSN:
1064-8275; 1095-7197
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/110823699
Appears in Collections:
Articles; KAUST Supercomputing Laboratory (KSL); KAUST Supercomputing Laboratory (KSL)

Full metadata record

DC FieldValue Language
dc.contributor.authorHaidar, Azzamen
dc.contributor.authorLtaief, Hatemen
dc.contributor.authorDongarra, Jacken
dc.date.accessioned2015-05-25T08:28:46Zen
dc.date.available2015-05-25T08:28:46Zen
dc.date.issued2012-01en
dc.identifier.citationToward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem 2012, 34 (6):C249 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/110823699en
dc.identifier.urihttp://hdl.handle.net/10754/555650en
dc.description.abstractClassical solvers for the dense symmetric eigenvalue problem suffer from the first step, which involves a reduction to tridiagonal form that is dominated by the cost of accessing memory during the panel factorization. The solution is to reduce the matrix to a banded form, which then requires the eigenvalues of the banded matrix to be computed. The standard divide and conquer algorithm can be modified for this purpose. The paper combines this insight with tile algorithms that can be scheduled via a dynamic runtime system to multicore architectures. A detailed analysis of performance and accuracy is included. Performance improvements of 14-fold and 4-fold speedups are reported relative to LAPACK and Intel's Math Kernel Library.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/110823699en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectdivide and conqueren
dc.subjectsymmetric eigenvalue solveren
dc.subjecttile algorithmsen
dc.subjectdynamic schedulingen
dc.titleToward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problemen
dc.typeArticleen
dc.contributor.departmentKAUST Supercomputing Laboratory (KSL)en
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TNen
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TNen
dc.contributor.institutionSchool of Mathematics and School of Computer Science, University of Manchester, Manchester, UKen
kaust.authorLtaief, Hatemen
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