Implementing a New Dense Symmetric Eigensolver on Multicore Systems
Type
ThesisAuthors
Sukkari, Dalal E.Advisors
Keyes, David E.
Committee members
Alouini, Mohamed-Slim
Laleg-Kirati, Taous-Meriem

Ltaief, Hatem

Date
2013-07Embargo End Date
2014-07-01Permanent link to this record
http://hdl.handle.net/10754/296952
Metadata
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At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis became available to the public after the expiration of the embargo on 2014-07-01.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.Citation
Sukkari, D. E. (2013). Implementing a New Dense Symmetric Eigensolver on Multicore Systems. KAUST Research Repository. https://doi.org/10.25781/KAUST-ENI4Jae974a485f413a2113503eed53cd6c53
10.25781/KAUST-ENI4J