Title | **A bivariate preprocessing paradigm for the Buchberger–Möller algorithm** |

Author(s) | Tian Dong, Xuhui Wang, Shugong Zhang |

Type | Article in Journal |

Abstract | For the last almost three decades, since the famous Buchberger–Möller (BM) algorithm emerged, there has been wide interest in vanishing ideals of points and associated interpolation polynomials. Our paradigm is based on the theory of bivariate polynomial interpolation on cartesian point sets that gives us a related degree reducing interpolation monomial and Newton bases directly. Since the bases are involved in the computation process as well as contained in the final output of the BM algorithm, our paradigm obviously simplifies the computation and accelerates the BM process. The experiments show that the paradigm is best suited for the computation over finite prime fields that have many applications. |

Keywords | Buchberger–Möller algorithm, Bivariate Lagrange interpolation, Degree reducing interpolation space, Cartesian set |

ISSN | 0377-0427 |

URL |
http://www.sciencedirect.com/science/article/pii/S0377042710002438 |

Language | English |

Journal | Journal of Computational and Applied Mathematics |

Volume | 234 |

Number | 12 |

Pages | 3344 - 3355 |

Year | 2010 |

Edition | 0 |

Translation |
No |

Refereed |
No |