2015/11/19 by Wenyuan Wu, Zhonggang Zeng · 2 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Computation #Dixon's factorization method #Factorization #Factorization of polynomials #Incomplete LU factorization #Lipschitz continuity #Numerical Methods and Algorithms #Numerical analysis #Polynomial #Polynomial and algebraic computation #Square-free polynomial #cs.NA #math.NA #msc:12Y05 #msc:13P05 #msc:65F22 #msc:65H04 #msc:65J20
paper · pdf · doi:10.1007/s10208-015-9289-1
crossref issued 2015/11/19 · crossref published 2015/11/19 · crossref published-online 2015/11/19 · openalex publication_date 2015/11/19 · crossref created 2015/11/19 · openalex created_date 2016/06/24 · crossref published-print 2017/02/01 · arxiv created 2021/03/08 · arxiv updated 2021/03/09 · crossref deposited 2023/08/15 · crossref indexed 2026/01/27 · openalex updated_date 2026/08/05
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper formulates the notion of numerical factorization based on the geometry of polynomial spaces and the stratification of factorization manifolds. Furthermore, this paper establishes the existence, uniqueness, Lipschitz continuity, condition number, and convergence of the numerical factorization to the underlying exact factorization, leading to a robust and efficient algorithm with a MATLAB implementation capable of accurate polynomial factorizations using floating point arithmetic even if the coefficients are perturbed.