HPC Fellowship: Communicationavoiding Linear Algebra
Presenter:
Mark Hoemmen
(University of California, Berkeley)

Doctoral Research Showcase Session
Wednesday, 04:00PM  04:30PM

Room 17A/17B

Abstract:
Communication dominates the performance of Krylov subspace methods
(KSMs), which are often used to solve large, sparse linear systems and
eigenvalue problems. Thus, we have developed communicationavoiding
KSMs, which are rearrangements of existing KSMs, such that a single
iteration of the new method accomplishes the same work as several
steps of the related ordinary KSM, but has the communication cost of
only one step. These rearrangements affect numerical stability, so I
have investigated ways to improve stability without sacrificing
performance. My advisor and I have also developed novel
preconditioned versions of the methods, by identifying both the
necessary computational kernels in the preconditioned case, as well as
a category of nontrivial preconditioners (those with offdiagonal
blocks of low rank) that work with these kernels and are known to be
effective for an important class of problems. Predictions suggest
speedups on a variety of platforms, especially on lowercost,
lowerpower hardware.