Structured Low Rank Approximation of a Bezout Matrix

被引：0
|
作者：
Sun, Dongxia [1 ]
Zhi, Lihong [1 ]
机构：
[1] Acad Mil Med Sci, Key Lab Math Mech, Beijing 100080, Peoples R China
来源：
MATHEMATICS IN COMPUTER SCIENCE | 2007年 / 1卷 / 02期
基金：
美国国家科学基金会;
关键词：
Bezout matrix; approximate greatest common divisor; structured nonlinear total least squares; symbolic/numeric hybrid method;
D O I：
10.1007/s11786-007-0014-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The task of determining the approximate greatest common divisor (GCD) of more than two univariate polynomials with inexact coefficients can be formulated as computing for a given Bezout matrix a new Bezout matrix of lower rank whose entries are near the corresponding entries of that input matrix. We present an algorithm based on a version of structured nonlinear total least squares (SNTLS) method for computing approximate GCD and demonstrate the practical performance of our algorithm on a diverse set of univariate polynomials.
引用
收藏
页码：427 / 437
页数：11
相关论文
共 50 条
  • [41] Approximation Schemes for Low-rank Binary Matrix Approximation Problems
    Fomin, Fedor, V
    Golovach, Petr A.
    Lokshtanov, Daniel
    Panolan, Fahad
    Saurabh, Saket
    ACM TRANSACTIONS ON ALGORITHMS, 2020, 16 (01)
  • [42] Lower bounds for the low-rank matrix approximation
    Jicheng Li
    Zisheng Liu
    Guo Li
    Journal of Inequalities and Applications, 2017
  • [43] Low-rank matrix approximation in the infinity norm
    Gillis, Nicolas
    Shitov, Yaroslav
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 581 (367-382) : 367 - 382
  • [44] Parameterized low-rank binary matrix approximation
    Fomin, Fedor, V
    Golovach, Petr A.
    Panolan, Fahad
    DATA MINING AND KNOWLEDGE DISCOVERY, 2020, 34 (02) : 478 - 532
  • [45] Nonnegative low rank matrix approximation for nonnegative matrices
    Song, Guang-Jing
    Ng, Michael K.
    APPLIED MATHEMATICS LETTERS, 2020, 105
  • [46] Convex Local Sensitive Low Rank Matrix Approximation
    Li, Chong-Ya
    Zhu, Lin
    Bao, Wen-Zheng
    Jiang, Yong-Li
    Yuan, Chang-An
    Huang, De-Shuang
    2017 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN), 2017, : 256 - 261
  • [47] Low rank approximation solution of a class of matrix equation
    Duan, Xuefeng
    Ding, Zhenya
    Zhang, Xinjun
    PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE OF MATRICES AND OPERATORS (MAO 2012), 2012, : 174 - 177
  • [48] Low-rank approximation pursuit for matrix completion
    Xu, An-Bao
    Xie, Dongxiu
    MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2017, 95 : 77 - 89
  • [49] Lower bounds for the low-rank matrix approximation
    Li, Jicheng
    Liu, Zisheng
    Li, Guo
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
  • [50] Low-Rank Matrix Approximation with Manifold Regularization
    Zhang, Zhenyue
    Zhao, Keke
    IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2013, 35 (07) : 1717 - 1729
12345