@techreport{oai:ipsj.ixsq.nii.ac.jp:00028645,
 author = {森, 大介 and 山本, 有作 and 張紹良 and Daisuke, Mori and Yusaku, Yamamoto and Shao-Liang, Zhang},
 issue = {99(2008-HPC-117)},
 month = {Oct},
 note = {従来， QR 分解を計算するに当たって，直交性の高い Q が得られることからハウスホルダー変換が用いられてきた．しかし，並列計算によって高速化を図る際に，アルゴリズムの強い遂次性から十分な並列性能が発揮できたとは言えない．そこヘ近年，並列粒度の高い AllReduce アルゴリズムが提案された．このアルゴリズムは行列を上下に分割してそれぞれに対して QR 分解を行うことにより，並列粒度の増大を可能としている． AllReduce アルゴリズムは様々な QR 分解手法に適用できるが，本稿ではハウスホルダー変換による手法に言及し，従来の手法と AllReduce アルゴリズムを用いた手法の性能の比較ならびに精度の比較を行う．, Up to now, the Householder QR algorithm has been one of preferred methods for QR factorization because of its high orthogonality of Q. However, due to its strong sequential nature, it is not straightforward to accelerate the algorithm by parallel computation. Recently the AllRedece algorithm, which has large grain size, was proposed. This algorithm makes it possible to increase the grain size by dividing the target matrix into the upper and the lower submatrices and performing the QR factorization of each submatrix independently. While the AllReduce algorithm is applicable to various QR factorization methods, we focus on application to the Householder QR algorithm in this report. We will compare the performance and the accuracy of the conventional method and the AllReduce algorithm.},
 title = {ハウスホルダーQR分解のためのAllReduceアルゴリズムの性能と精度},
 year = {2008}
}