SC Conference - Activity Details

HPC Fellowship: Communication-avoiding Linear Algebra

Mark Hoemmen  (University of California, Berkeley)
Doctoral Research Showcase Session
Wednesday,  04:00PM - 04:30PM
Room 17A/17B
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 communication-avoiding 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 off-diagonal 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 lower-cost, lower-power hardware.
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