### 抄録

This paper is concerned with a robust geometric predicate for the 2D orientation problem. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi, which provably outputs a result faithfully rounded from the exact value of the summation of floating-point numbers. We optimize their algorithm for applying it to the 2D orientation problem which requires only a correct sign of a determinant of a 3×3 matrix. Numerical results illustrate that our algorithm works fairly faster than the state-of-the-art algorithm in various cases.

元の言語 | English |
---|---|

ページ（範囲） | 215-231 |

ページ数 | 17 |

ジャーナル | Japan Journal of Industrial and Applied Mathematics |

巻 | 26 |

発行部数 | 2-3 |

出版物ステータス | Published - 2009 10 |

外部発表 | Yes |

### ASJC Scopus subject areas

- Applied Mathematics
- Engineering(all)

### これを引用

*Japan Journal of Industrial and Applied Mathematics*,

*26*(2-3), 215-231.

**Adaptive and efficient algorithm for 2D orientation problem.** / Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin'ichi.

研究成果: Article

*Japan Journal of Industrial and Applied Mathematics*, 巻. 26, 番号 2-3, pp. 215-231.

}

TY - JOUR

T1 - Adaptive and efficient algorithm for 2D orientation problem

AU - Ozaki, Katsuhisa

AU - Ogita, Takeshi

AU - Rump, Siegfried M.

AU - Oishi, Shin'ichi

PY - 2009/10

Y1 - 2009/10

N2 - This paper is concerned with a robust geometric predicate for the 2D orientation problem. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi, which provably outputs a result faithfully rounded from the exact value of the summation of floating-point numbers. We optimize their algorithm for applying it to the 2D orientation problem which requires only a correct sign of a determinant of a 3×3 matrix. Numerical results illustrate that our algorithm works fairly faster than the state-of-the-art algorithm in various cases.

AB - This paper is concerned with a robust geometric predicate for the 2D orientation problem. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi, which provably outputs a result faithfully rounded from the exact value of the summation of floating-point numbers. We optimize their algorithm for applying it to the 2D orientation problem which requires only a correct sign of a determinant of a 3×3 matrix. Numerical results illustrate that our algorithm works fairly faster than the state-of-the-art algorithm in various cases.

KW - 2D orientation problem

KW - Accurate algorithm

KW - Floating-point arithmetic

KW - Robust geometric predicate

UR - http://www.scopus.com/inward/record.url?scp=77149180779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77149180779&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77149180779

VL - 26

SP - 215

EP - 231

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 2-3

ER -