## 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 |
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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

Other | 5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2014 |
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国/地域 | United States |

City | New Orleans |

Period | 14/11/17 → … |

## 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