Title | **Complete numerical isolation of real roots in zero-dimensional triangular systems** |

Author(s) | Jin-San Cheng, Xiao Shan Gao, Chee-K. K. Yap |

Type | Article in Journal |

Abstract | We present a complete numerical algorithm for isolating all the real zeros of a zero-dimensional triangular polynomial system F_n ⊆ Z [ x_1 … x_n ] . Our system F n is general, with no further assumptions. In particular, our algorithm successfully treats multiple zeros directly in such systems. A key idea is to introduce evaluation bounds and sleeve bounds. We also present a much more efficient algorithm for zero-dimensional triangular systems without multiple roots. We implemented our algorithms, and promising experimental results are shown. |

Keywords | Triangular system, Real zero isolation, Sleeve bound, Evaluation bound |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S074771710800120X |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 44 |

Number | 7 |

Pages | 768 - 785 |

Year | 2009 |

Note | International Symposium on Symbolic and Algebraic Computation |

Edition | 0 |

Translation |
No |

Refereed |
No |