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DTSTART;TZID=Europe/Stockholm:20190618T083000
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UID:isc_hpc_ISC High Performance 2019_sess182_post128@linklings.com
SUMMARY:(RP10) High-Performance Computing of Thin QR Decomposition on Par
allel Systems
DESCRIPTION:Research Poster\nConference Pass, Parallel Algorithms\n\n(RP10
) High-Performance Computing of Thin QR Decomposition on Parallel Systems
\n\nTerao, Ozaki, Ogita\n\nThis poster aims to propose the preconditioned
Cholesky QR algorithms for thin QR decomposition (also called economy size
QR decomposition). CholeskyQR is known as a fast algorithm employed for t
hin QR decomposition, and CholeskyQR2 is recently proposed for improving t
he orthogonality of a Q-factor computed by CholeskyQR. Although such Chole
sky QR algorithms can efficiently be implemented in high-performance compu
ting environments, they are not applicable for ill-conditioned matrices, a
s compared to the Householder QR and the Gram-Schmidt algorithms. To addre
ss this problem, we propose two algorithms named LU-Cholesky QR and Robust
Cholesky QR. On LU-Chlesky QR, we apply the concept of LU decomposition t
o the Cholesky QR algorithms, i.e., the idea is to use LU-factors of a giv
en matrix as preconditioning before applying Cholesky decomposition. Robus
t Cholesky QR uses a part of Cholesky factor for constructing the precondi
tioner when Cholesky decomposition breaks down. The feature of Robust Chol
esky 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 ma
trix is moderately well-conditioned. Numerical examples provided in this p
oster illustrate the efficiency of the proposed algorithms in parallel com
puting on distributed memory computers.
URL:https://2019.isc-program.com/presentation/?id=post128&sess=sess182
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