From an approximate to an exact absolute polynomial factorization

被引：15
|
作者：
Cheze, Guillaume [1 ]
Galligo, Andre [1 ]
机构：
[1] Univ Nice, Math Lab, F-06108 Nice 2, France
来源：
JOURNAL OF SYMBOLIC COMPUTATION | 2006年 / 41卷 / 06期
关键词：
absolute factorization; algebraic integers; vandermonde matrix;
D O I：
10.1016/j.jsc.2005.11.004
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We propose an algorithm for computing an exact absolute factorization of a bivariate polynomial from an approximate one. This algorithm is based on some properties of the algebraic integers over Z and is certified. It relies on a study of the perturbations in a Vandermonde system. We provide a sufficient condition on the precision of the approximate factors, depending only on the height and the degree of the polynomial. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码：682 / 696
页数：15
相关论文
共 50 条
  • [1] Exact Polynomial Factorization by Approximate High Degree Algebraic Numbers
    Chen Jing-wei
    Feng Yong
    Qin Xiao-lin
    Zhang Jing-zhong
    SNC'09: PROCEEDINGS OF THE 2009 INTERNATIONAL WORKSHOP ON SYMBOLIC-NUMERIC COMPUTATION, 2009, : 21 - 28
  • [2] The Approximate Irreducible Factorization of a Univariate Polynomial. Revisited
    Zeng, Zhonggang
    ISSAC2009: PROCEEDINGS OF THE 2009 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, 2009, : 367 - 374
  • [3] Polynomial GCD and Factorization Via Approximate Grobner Bases
    Lichtblau, Daniel
    12TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND NUMERIC ALGORITHMS FOR SCIENTIFIC COMPUTING (SYNASC 2010), 2011, : 29 - 36
  • [4] 'New algorithms for exact and approximate polynomial decomposition
    Giesbrecht, Aark
    May, John
    SYMBOLIC-NUMERIC COMPUTATION, 2007, : 99 - +
  • [5] Unconstrained Parametric Minimization of a Polynomial: Approximate and Exact
    Liang, S.
    Jeffrey, D. J.
    COMPUTER MATHEMATICS, 2008, 5081 : 22 - 31
  • [6] Modular Las Vegas algorithms for polynomial absolute factorization
    Bertone, Cristina
    Cheze, Guillaume
    Galligo, Andre
    JOURNAL OF SYMBOLIC COMPUTATION, 2010, 45 (12) : 1280 - 1295
  • [7] Exact bivariate polynomial factorization over ℚ by approximation of roots
    Yong Feng
    Wenyuan Wu
    Jingzhong Zhang
    Jingwei Chen
    Journal of Systems Science and Complexity, 2015, 28 : 243 - 260
  • [8] Approximate stable multidimensional polynomial factorization into linear m-D polynomial factors
    Mastorakis, NE
    KYBERNETIKA, 1996, 32 (03) : 275 - 288
  • [9] Exact bivariate polynomial factorization over a"e by approximation of roots
    Feng Yong
    Wu Wenyuan
    Zhang Jingzhong
    Chen Jingwei
    JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2015, 28 (01) : 243 - 260
  • [10] Exact Bivariate Polynomial Factorization over Q by Approximation of Roots
    FENG Yong
    WU Wenyuan
    ZHANG Jingzhong
    CHEN Jingwei
    Journal of Systems Science & Complexity, 2015, 28 (01) : 243 - 260
12345