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DTSTART:19700308T020000
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DTSTAMP:20200227T164259Z
LOCATION:Analog 1\, 2
DTSTART;TZID=Europe/Stockholm:20190619T101000
DTEND;TZID=Europe/Stockholm:20190619T110000
UID:isc_hpc_ISC High Performance 2019_sess251_post128@linklings.com
SUMMARY:(RP10) High-Performance Computing of Thin QR Decomposition on Par
allel Systems
DESCRIPTION:HPC in Asia\n\n(RP10) High-Performance Computing of Thin QR D
ecomposition on Parallel Systems\n\nTerao, Ozaki, Ogita\n\nThis poster aim
s to propose the preconditioned Cholesky QR algorithms for thin QR decompo
sition (also called economy size QR decomposition). CholeskyQR is known as
a fast algorithm employed for thin QR decomposition, and CholeskyQR2 is r
ecently proposed for improving the orthogonality of a Q-factor computed by
CholeskyQR. Although such Cholesky QR algorithms can efficiently be imple
mented in high-performance computing environments, they are not applicable
for ill-conditioned matrices, as compared to the Householder QR and the G
ram-Schmidt algorithms. To address this problem, we propose two algorithms
named LU-Cholesky QR and Robust Cholesky QR. On LU-Chlesky QR, we apply t
he concept of LU decomposition to the Cholesky QR algorithms, i.e., the id
ea is to use LU-factors of a given matrix as preconditioning before applyi
ng Cholesky decomposition. Robust Cholesky QR uses a part of Cholesky fact
or for constructing the preconditioner when Cholesky decomposition breaks
down. The feature of Robust Cholesky QR is its adaptiveness for difficulty
of problems. In fact, the cost for the preconditioning in Robust Cholesky
QR can be omitted if a given matrix is moderately well-conditioned. Numer
ical examples provided in this poster illustrate the efficiency of the pro
posed algorithms in parallel computing on distributed memory computers.\n\
nPasses: Conference Pass, Parallel Algorithms\n\nTag: Conference Pass, Par
allel Algorithms
URL:https://2019.isc-program.com/presentation/?id=post128&sess=sess251
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