Return to search

Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem

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

Identiferoai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2009-05-139
Date03 September 2009
CreatorsPoulson, Jack Lesly
Source SetsUniversity of Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Formatapplication/pdf

Page generated in 0.002 seconds