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DTSTART:20180325T030000
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DTSTAMP:20200925T162010Z
UID:5a99537338a43910704865@ist.ac.at
DTSTART:20180404T100000
DTEND:20180404T110000
DESCRIPTION:Speaker: Erin Carson\nhosted by Chris Wojtan\nAbstract: Sparse
linear algebra problems\, typically solved using iterative methods\, are u
biquitous throughout scientific and data analysis applications and are oft
en the most expensive computations in large-scale codes due to the high co
st of data movement. Approaches to improving the performance of iterative
methods typically involve modifying or restructuring the algorithm to redu
ce or hide this cost. Such modifications can\, however\, result in drastic
ally different behavior in terms of convergence rate and accuracy. A clear
\, thorough understanding of how inexact computations\, due to either fini
te precision error or intentional approximation\, affect numerical behavio
r is thus imperative in balancing the tradeoffs between accuracy\, converg
ence rate\, and performance in practical settings.In this talk\, we focus
on two general classes of iterative methods for solving linear systems: Kr
ylov subspace methods and iterative refinement. We present bounds on the a
ttainable accuracy and convergence rate in finite precision s-step and pip
elined Krylov subspace methods\, two popular variants designed for high pe
rformance. For s-step methods\, we demonstrate that our bounds on attainab
le accuracy can lead to adaptive approaches that both achieve efficient pa
rallel performance and ensure that a user-specified accuracy is attained.
We present two such adaptive approaches\, including a residual replacement
scheme and a variable s-step technique in which the parameter s is chosen
dynamically throughout the iterations. Motivated by the recent trend of m
ultiprecision capabilities in hardware\, we present new forward and backwa
rd error bounds for a general iterative refinement scheme using three prec
isions. The analysis suggests that on architectures where half precision i
s implemented efficiently\, it is possible to solve certain linear systems
up to twice as fast and to greater accuracy.As we push toward exascale le
vel computing and beyond\, designing efficient\, accurate algorithms for e
merging architectures and applications is of utmost importance. We discuss
extensions to machine learning and data analysis applications\, the devel
opment of numerical autotuning tools\, and the broader challenge of unders
tanding what increasingly large problem sizes will mean for finite precisi
on computation both in theory and practice.
LOCATION:Mondi Seminar Room 2\, Central Building\, IST Austria
ORGANIZER:pdelreal@ist.ac.at
SUMMARY:Sparse Linear Algebra in the Exascale Era
URL:https://talks-calendar.app.ist.ac.at/events/1174
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