Abstract

The input to our algorithm is a multivariate polynomial, whose complex rational coe#cients are considered imprecise with an unknown error that causes f to be irreducible over the complex numbers C. We seek to perturb the coe#cients by a small quantitity such that the resulting polynomial factors over C. Ideally, one would like to minimize the perturbation in some selected distance measure, but no e#cient algorithm for that is known. We give a numerical multivariate greatest common divisor algorithm and use it on a numerical variant of algorithms by W. M. Ruppert and S. Gao. Our numerical factorizer makes repeated use of singular value decompositions. We demonstrate on a significant body of experimental data that our algorithm is practical and can find factorizable polynomials within a distance that is about the same in relative magnitude as the input error, even when the relative error in the input is substantial (10 -3 ).

Citations