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DTSTAMP:20181221T160904Z
LOCATION:C2/3/4 Ballroom
DTSTART;TZID=America/Chicago:20181113T083000
DTEND;TZID=America/Chicago:20181113T170000
UID:submissions.supercomputing.org_SC18_sess322_post193@linklings.com
SUMMARY:Performance Evaluation of the Shifted Cholesky QR Algorithm for Il
 l-Conditioned Matrices
DESCRIPTION:Poster\nTech Program Reg Pass, Exhibits Reg Pass\n\nPerformanc
 e Evaluation of the Shifted Cholesky QR Algorithm for Ill-Conditioned Matr
 ices\n\nFukaya, Kannan, Nakatsukasa, Yamamoto, Yanagisawa\n\nThe Cholesky 
 QR algorithm, which computes the QR factorization of a matrix, is a simple
  yet efficient algorithm for high-performance computing. However it suffer
 s from numerical instability. In a recent work, this instability has been 
 remedied by repeating Cholesky QR twice (CholeskyQR2).  ChokeskyQR2, howev
 er, is still prone to numerical breakdown when applied to ill-conditioned 
 matrices. To overcome this limitation, we introduce a shifting technique t
 o Cholesky QR and use it as a preconditioning step before CholeskyQR2. The
  key idea is that Cholesky QR with shift reduces the condition number of t
 he input matrix. We call the resulting algorithm shifted CholeskyQR3, whic
 h is still simple and only requires double precision arithmetic. In this p
 oster, we present the results of our performance evaluation of shifted Cho
 leskyQR3. We demonstrate that shifted CholeskyQR3 accurately computes the 
 QR factorization of ill-conditioned matrices and that it outperforms other
  conventional algorithms in execution time.
URL:https://sc18.supercomputing.org/presentation/?id=post193&sess=sess322
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