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DTSTART:19700308T020000
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DTSTAMP:20210518T152204Z
LOCATION:Substanz 1\, 2
DTSTART;TZID=Europe/Stockholm:20190618T083000
DTEND;TZID=Europe/Stockholm:20190618T100000
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\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 dec
omposition (also called economy size QR decomposition). CholeskyQR is know
n as a fast algorithm employed for thin QR decomposition, and CholeskyQR2
is recently proposed for improving the orthogonality of a Q-factor compute
d by CholeskyQR. Although such Cholesky QR algorithms can efficiently be i
mplemented in high-performance computing environments, they are not applic
able for ill-conditioned matrices, as compared to the Householder QR and t
he Gram-Schmidt algorithms. To address this problem, we propose two algori
thms named LU-Cholesky QR and Robust Cholesky QR. On LU-Chlesky QR, we app
ly the concept of LU decomposition to the Cholesky QR algorithms, i.e., th
e idea is to use LU-factors of a given matrix as preconditioning before ap
plying Cholesky decomposition. Robust Cholesky QR uses a part of Cholesky
factor for constructing the preconditioner when Cholesky decomposition bre
aks down. The feature of Robust Cholesky QR is its adaptiveness for diffic
ulty of problems. In fact, the cost for the preconditioning in Robust Chol
esky QR can be omitted if a given matrix is moderately well-conditioned. N
umerical examples provided in this poster illustrate the efficiency of the
proposed algorithms in parallel computing on distributed memory computers
.\n\nPasses: Conference Pass\n\nTag: Parallel Algorithms
URL:https://2019.isc-program.com/presentation/?id=post128&sess=sess182
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