### 抄録

The numerical computations with guaranteed accuracy called verified numerical computations are studied, herein. We focus on an accurate numerical solution for dense linear systems of the form Ax = b and error bound of in supercomputing, where is an approximate solution. First, we implemented accurate algorithms for a matrix-vector product for parallel and distributed computing, and then, applied them to iterative refinements. Next, we implemented verified numerical computations using the Parallel Basic Linear Algebra Subprograms (PBLAS) and the Scalable Linear Algebra Package library (ScaLAPACK). Numerical examples of the verified numerical computations for linear systems are presented using the Fujitsu FX100 supercomputer. They clearly illustrate the efficiency of the verified numerical computations.

元の言語 | English |
---|---|

記事番号 | 012014 |

ジャーナル | Journal of Physics: Conference Series |

巻 | 1218 |

発行部数 | 1 |

DOI | |

出版物ステータス | Published - 2019 5 31 |

イベント | 3rd International Conference on Mathematics; Pure, Applied and Computation, ICoMPAC 2018 - Surabaya, Indonesia 継続期間: 2018 10 20 → … |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### これを引用

**Verified numerical computations for dense linear systems in supercomputing.** / Ozaki, Katsuhisa.

研究成果: Conference article

}

TY - JOUR

T1 - Verified numerical computations for dense linear systems in supercomputing

AU - Ozaki, Katsuhisa

PY - 2019/5/31

Y1 - 2019/5/31

N2 - The numerical computations with guaranteed accuracy called verified numerical computations are studied, herein. We focus on an accurate numerical solution for dense linear systems of the form Ax = b and error bound of in supercomputing, where is an approximate solution. First, we implemented accurate algorithms for a matrix-vector product for parallel and distributed computing, and then, applied them to iterative refinements. Next, we implemented verified numerical computations using the Parallel Basic Linear Algebra Subprograms (PBLAS) and the Scalable Linear Algebra Package library (ScaLAPACK). Numerical examples of the verified numerical computations for linear systems are presented using the Fujitsu FX100 supercomputer. They clearly illustrate the efficiency of the verified numerical computations.

AB - The numerical computations with guaranteed accuracy called verified numerical computations are studied, herein. We focus on an accurate numerical solution for dense linear systems of the form Ax = b and error bound of in supercomputing, where is an approximate solution. First, we implemented accurate algorithms for a matrix-vector product for parallel and distributed computing, and then, applied them to iterative refinements. Next, we implemented verified numerical computations using the Parallel Basic Linear Algebra Subprograms (PBLAS) and the Scalable Linear Algebra Package library (ScaLAPACK). Numerical examples of the verified numerical computations for linear systems are presented using the Fujitsu FX100 supercomputer. They clearly illustrate the efficiency of the verified numerical computations.

UR - http://www.scopus.com/inward/record.url?scp=85067825200&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067825200&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1218/1/012014

DO - 10.1088/1742-6596/1218/1/012014

M3 - Conference article

AN - SCOPUS:85067825200

VL - 1218

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012014

ER -