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DTSTAMP:20260522T150111Z
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DTSTART;TZID=America/Chicago:20181115T083000
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UID:submissions.supercomputing.org_SC18_sess324_post193@linklings.com
SUMMARY:Performance Evaluation of the Shifted Cholesky QR Algorithm for Il
 l-Conditioned Matrices
DESCRIPTION:Takeshi Fukaya (Hokkaido University); Ramaseshan Kannan (Arup 
 UK); Yuji Nakatsukasa (National Institute of Informatics, Japan); Yusaku Y
 amamoto (University of Electro-Communications, Japan); and Yuka Yanagisawa
  (Waseda University)\n\nThe Cholesky QR algorithm, which computes the QR f
 actorization of a matrix, is a simple yet efficient algorithm for high-per
 formance computing. However it suffers from numerical instability. In a re
 cent work, this instability has been remedied by repeating Cholesky QR twi
 ce (CholeskyQR2).  ChokeskyQR2, however, is still prone to numerical break
 down when applied to ill-conditioned matrices. To overcome this limitation
 , we introduce a shifting technique to Cholesky QR and use it as a precond
 itioning step before CholeskyQR2. The key idea is that Cholesky QR with sh
 ift reduces the condition number of the input matrix. We call the resultin
 g algorithm shifted CholeskyQR3, which is still simple and only requires d
 ouble precision arithmetic. In this poster, we present the results of our 
 performance evaluation of shifted CholeskyQR3. We demonstrate that shifted
  CholeskyQR3 accurately computes the QR factorization of ill-conditioned m
 atrices and that it outperforms other conventional algorithms in execution
  time.\n\nRegistration Category: Tech Program Reg Pass, Exhibits Reg Pass\
 n\n
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