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DTSTART:19700308T020000
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DTSTAMP:20260522T150117Z
LOCATION:D161
DTSTART;TZID=America/Chicago:20181112T140000
DTEND;TZID=America/Chicago:20181112T142000
UID:submissions.supercomputing.org_SC18_sess158_ws_lasalss104@linklings.co
 m
SUMMARY:Iterative Randomized Algorithms for Low Rank Approximation of Tera
 scale Matrices with Small Spectral Gaps
DESCRIPTION:Chander J. Iyer (Rensselaer Polytechnic Institute, Yahoo! Rese
 arch); Alex Gittens and Christopher D. Carothers (Rensselaer Polytechnic I
 nstitute); and Petros Drineas (Purdue University)\n\nRandomized approaches
  for low rank matrix approximations have become popular in recent years an
 d often offer significant advantages over classical algorithms because of 
 their scalability and numerical robustness on distributed memory platforms
 . We present a distributed implementation of randomized block iterative me
 thods to compute low rank matrix approximations for dense tera-scale matri
 ces. We are particularly interested in the behavior of randomized block it
 erative methods on matrices with small spectral gaps. Our distributed impl
 ementation is based on four iterative algorithms: block subspace iteration
 , the block Lanczos method, the block Lanczos method with explicit restart
 s, and the thick-restarted block Lanczos method. We analyze the scalabilit
 y and numerical stability of the four block iterative methods and demonstr
 ate the performance of these methods for various choices of the spectral g
 ap. Performance studies demonstrate superior runtimes of the block Lanczos
  algorithms over the subspace power iteration approach on (up to) 16,384 c
 ores of AMOS, Rensselaer's IBM Blue Gene/Q supercomputer.\n\nTag: Algorith
 ms, Heterogeneous Systems, Resiliency\n\nRegistration Category: Workshop R
 eg Pass\n\nSession Chairs: Vassil Alexandrov (Hartree Centre, STFC); Jack 
 Dongarra (University of Tennessee, Knoxville; Oak Ridge National Laborator
 y (ORNL)); Christian Engelmann (Oak Ridge National Laboratory (ORNL)); and
  Al Geist (Oak Ridge National Laboratory (ORNL))\n\n
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