Title

The Numerical Factorization of Polynomials

Document Type

Article

Publication Date

2-1-2017

Abstract

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.

DOI

10.1007/s10208-015-9289-1

Publication Title

Foundations of Computational Mathematics

Volume Number

17

Issue Number

1

First Page

259

Last Page

286

ISSN

16153375

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