Pseudofactors of multivariate polynomials

Abstract

We treat pseudo-factorization of a multivariate polynomial p over C as an overdetermined bilinear system for the coefficients of the factors. If the specified data (coefficients of p) are sufficiently close to the manifold of consistent data we project onto it by solving a well-chosen subsystem (otherwise we quit). On the manifold, we reduce the backward error by a linearized minimization procedure. The resulting algorithm appears to extend the range of treatable cases - in terms of number of variables and total degree - considerably.