CholeskyQR2: A Simple and Communication-Avoiding Algorithm for Computing a Tall-Skinny QR Factorization on a Large-Scale Parallel System

Takeshi Fukaya, Yuji Nakatsukasa, Yuka Yanagisawa, Yusaku Yamamoto

研究成果: Conference contribution

19 被引用数 (Scopus)

抄録

Designing communication-avoiding algorithms is crucial for high performance computing on a large-scale parallel system. The TSQR algorithm is a communication-avoiding algorithm for computing a tall-skinny QR factorization, and TSQR is known to be much faster and as stable as the classical Householder QR algorithm. The Cholesky QR algorithm is another very simple and fast communication-avoiding algorithm, but rarely used in practice because of its numerical instability. Our recent work points out that an algorithm that simply repeats Cholesky QR twice, which we call CholeskyQR2, gives excellent accuracy for a wide range of matrices arising in practice. Although the communication cost of CholeskyQR2 is twice that of TSQR, it has an advantage that its reduction operation is addition whereas that of TSQR is a QR factorization, whose high-performance implementation is more difficult. Thus, CholeskyQR2 can potentially be significantly faster than TSQR. Indeed, in our experiments using 16384 nodes of the K computer, CholeskyQR2 ran about three times faster than TSQR for a 4194304 × 64 matrix.

本文言語English
ホスト出版物のタイトルProceedings of ScalA 2014
ホスト出版物のサブタイトル5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - held in conjunction with SC 2014: The International Conference for High Performance Computing, Networking, Storage and Analysis
出版社Institute of Electrical and Electronics Engineers Inc.
ページ31-38
ページ数8
ISBN(電子版)9781479975624
DOI
出版ステータスPublished - 2014
イベント5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2014 - New Orleans, United States
継続期間: 2014 11月 17 → …

Other

Other5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2014
国/地域United States
CityNew Orleans
Period14/11/17 → …

ASJC Scopus subject areas

  • 計算理論と計算数学
  • コンピュータ ネットワークおよび通信
  • コンピュータ サイエンスの応用
  • ソフトウェア
  • 電子工学および電気工学

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