Extracting numerical factors of multivariate polynomials from Taylor expansions
Faculty of Sciences. Mathematics and Computer Science
New York, N.Y. , 2009
Proceedings of the International Workshop on Symbolic-Numeric Computation, August 3-5, 2009, Kyoto, Japan / Kai, H. [edit.]; et al. [edit.]
University of Antwerp
We present a method to extract factors of multivariate polynomials with complex coefficients in floating point arithmetic. We establish the connection between the reciprocal of a multivariate polynomial and its Taylor expansion. Since the multivariate Taylor coefficients are determined by the irreducible factors of the given polynomial, we reconstruct the factors from the Taylor expansion. As each irreducible factor, regardless of its multiplicity, can be separately extracted, our method can lead toward the complete numerical factorization of multivariate polynomials.