This thesis demonstrates an efficient parallel method of solving the generalized eigenvalue problem, KΦ = M ΦΛ, where K is symmetric and M is symmetric positive-definite, by first converting it to a standard eigenvalue problem, solving the standard eigenvalue problem, and back-transforming the results. An abstraction for parallel dense linear algebra is introduced along
with a new algorithm for forming A := U⁻ᵀ K U⁻¹ , where U is the Cholesky factor of M , that is up to twice as fast as the ScaLAPACK implementation. Additionally, large improvements over the PBLAS implementations of general
matrix-matrix multiplication and triangular solves with many right-hand sides are shown. Significant performance gains are also demonstrated for Cholesky
factorizations, and a case is made for using 2D-cyclic distributions with a distribution blocksize of one. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2009-05-139 |
| Date | 03 September 2009 |
| Creators | Poulson, Jack Lesly |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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