Implementing a New Dense Symmetric Eigensolver on Multicore Systems
AuthorsSukkari, Dalal E.
AdvisorsKeyes, David E.
Embargo End Date2014-07-01
Permanent link to this recordhttp://hdl.handle.net/10754/296952
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Access RestrictionsAt 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.
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  and LAPACK . 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.
CitationSukkari, D. E. (2013). Implementing a New Dense Symmetric Eigensolver on Multicore Systems. KAUST Research Repository. https://doi.org/10.25781/KAUST-ENI4J