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DTSTART:20180325T030000
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DTSTAMP:20260405T175602Z
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\, ISTA
ORGANIZER:pdelreal@ist.ac.at
SUMMARY:Erin Carson: Sparse Linear Algebra in the Exascale Era
URL:https://talks-calendar.ista.ac.at/events/1174
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