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DTSTART:20180325T030000
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DTSTAMP:20210120T170058Z
UID:5a96c0cb0338f816926510@ist.ac.at
DTSTART:20180302T090000
DTEND:20180302T100000
DESCRIPTION:Speaker: Erin Carson\nhosted by TBA\nAbstract: Sparse linear al
gebra problems\, typically solved using iterative methods\, are ubiquitous
throughout scientific and data analysis applications and are often the mo
st expensive computations in large-scale codes due to the high cost of dat
a movement. Approaches to improving the performance of iterative methods t
ypically involve modifying or restructuring the algorithm to reduce or hid
e this cost. Such modifications can\, however\, result in drastically diff
erent behavior in terms of convergence rate and accuracy. A clear\, thorou
gh understanding of how inexact computations\, due to either finite precis
ion error or intentional approximation\, affect numerical behavior is thus
imperative in balancing the tradeoffs between accuracy\, convergence rate
\, and performance in practical settings.In this talk\, we focus on two ge
neral classes of iterative methods for solving linear systems: Krylov subs
pace methods and iterative refinement. We present bounds on the attainable
accuracy and convergence rate in finite precision s-step and pipelined Kr
ylov subspace methods\, two popular variants designed for high performance
. For s-step methods\, we demonstrate that our bounds on attainable accura
cy can lead to adaptive approaches that both achieve efficient parallel pe
rformance and ensure that a user-specified accuracy is attained. We presen
t two such adaptive approaches\, including a residual replacement scheme a
nd a variable s-step technique in which the parameter s is chosen dynamica
lly throughout the iterations. Motivated by the recent trend of multipreci
sion capabilities in hardware\, we present new forward and backward error
bounds for a general iterative refinement scheme using three precisions. T
he analysis suggests that on architectures where half precision is impleme
nted efficiently\, it is possible to solve certain linear systems up to tw
ice as fast and to greater accuracy.As we push toward exascale level compu
ting and beyond\, designing efficient\, accurate algorithms for emerging a
rchitectures and applications is of utmost importance. We discuss extensio
ns to machine learning and data analysis applications\, the development of
numerical autotuning tools\, and the broader challenge of understanding w
hat increasingly large problem sizes will mean for finite precision comput
ation both in theory and practice.
LOCATION:Mondi Seminar Room 3\, 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/1126
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