  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.
