Implementing a New Dense Symmetric Eigensolver on Multicore Systems

Handle URI:
http://hdl.handle.net/10754/296952
Title:
Implementing a New Dense Symmetric Eigensolver on Multicore Systems
Authors:
Sukkari, Dalal E.
Abstract:
We present original advanced architecture implementations of the QDWHeig algo- rithm for solving dense symmetric eigenproblems. The algorithm (Y. Nakatsukasa and N. J. Higham, 2012) performs a spectral divide-and-conquer, which recursively divides the matrix into smaller submatrices by finding an invariant subspace for a subset of the spectrum. The main contribution of this thesis is to enhance the per- formance of QDWHeig algorithm by relying on a high performance kernels from PLASMA [1] and LAPACK [2]. We demonstrate the quality of the eigenpairs that are computed with the QDWHeig algorithm for many matrix types with different eigenvalue clustering. We then implement QDWHeig using kernels from LAPACK and PLASMA, and compare its performance against other divide-and-conquer sym- metric eigensolvers. The main part of QDWHeig is finding a polar decomposition. We introduce mixed precision to enhance the performance in finding the polar decom- position. Our evaluation considers speed and accuracy of the computed eigenvalues. Some applications require finding only a subspectrum of the eigenvalues; therefore we modify the algorithm to find the eigenpairs in a given interval of interest. An ex- perimental study shows significant improvement on the performance of our algorithm using mixed precision and PLASMA routines.
Advisors:
Keyes, David E. ( 0000-0002-4052-7224 )
Committee Member:
Alouini, Mohamed-Slim ( 0000-0003-4827-1793 ) ; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 ) ; Ltaief, Hatem ( 0000-0002-6897-1095 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
Jul-2013
Type:
Thesis
Appears in Collections:
Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorKeyes, David E.en
dc.contributor.authorSukkari, Dalal E.en
dc.date.accessioned2013-07-24T09:22:39Z-
dc.date.available2013-07-24T09:22:39Z-
dc.date.issued2013-07en
dc.identifier.urihttp://hdl.handle.net/10754/296952en
dc.description.abstractWe present original advanced architecture implementations of the QDWHeig algo- rithm for solving dense symmetric eigenproblems. The algorithm (Y. Nakatsukasa and N. J. Higham, 2012) performs a spectral divide-and-conquer, which recursively divides the matrix into smaller submatrices by finding an invariant subspace for a subset of the spectrum. The main contribution of this thesis is to enhance the per- formance of QDWHeig algorithm by relying on a high performance kernels from PLASMA [1] and LAPACK [2]. We demonstrate the quality of the eigenpairs that are computed with the QDWHeig algorithm for many matrix types with different eigenvalue clustering. We then implement QDWHeig using kernels from LAPACK and PLASMA, and compare its performance against other divide-and-conquer sym- metric eigensolvers. The main part of QDWHeig is finding a polar decomposition. We introduce mixed precision to enhance the performance in finding the polar decom- position. Our evaluation considers speed and accuracy of the computed eigenvalues. Some applications require finding only a subspectrum of the eigenvalues; therefore we modify the algorithm to find the eigenpairs in a given interval of interest. An ex- perimental study shows significant improvement on the performance of our algorithm using mixed precision and PLASMA routines.en
dc.language.isoenen
dc.subjectaccuracyen
dc.subjectperformanceen
dc.subjectimplementationen
dc.subjectplasmaen
dc.subjectlapacken
dc.subjecteigensolveren
dc.titleImplementing a New Dense Symmetric Eigensolver on Multicore Systemsen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberAlouini, Mohamed-Slimen
dc.contributor.committeememberLaleg-Kirati, Taous-Meriemen
dc.contributor.committeememberLtaief, Hatemen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id118549en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.