# Presentation

(RP10) High-Performance Computing of Thin QR Decomposition on Parallel Systems

SessionHPC in Asia Poster Session

Event Type

HPC in Asia

Parallel Algorithms

TimeWednesday, June 19th10:10am - 11am

LocationAnalog 1, 2

DescriptionThis 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 thin QR decomposition, and CholeskyQR2 is recently proposed for improving the orthogonality of a Q-factor computed by CholeskyQR. Although such Cholesky QR algorithms can efficiently be implemented in high-performance computing environments, they are not applicable for ill-conditioned matrices, as compared to the Householder QR and the Gram-Schmidt algorithms. To address 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 to the Cholesky QR algorithms, i.e., the idea is to use LU-factors of a given matrix as preconditioning before applying Cholesky decomposition. Robust Cholesky QR uses a part of Cholesky factor 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. Numerical examples provided in this poster illustrate the efficiency of the proposed algorithms in parallel computing on distributed memory computers.