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We propose three algorithms for approximate factorization of univariate polynomials over Z; the first one uses sums of powers of roots (SPR method), the second one utilizes factor-differentiated polynomials (FD method), and the third one is a robust but slow method (RS method). The SPR method is applicable to monic polynomials well but it is almost useless for non-monic polynomials unless their leading coefficients are sufficiently small. The FD method is applicable to both monic and non-monic polynomials, but it also becomes useless if both the leading and the tail coefficients increase. The RS method is applicable to any polynomial factorizable approximately over Z, but it is slow. We discuss two types of polynomials which are ill-conditioned for rootfinding, polynomials with close roots and Wilkinson-type polynomials. Furthermore, we consider briefly approximate factorization of multivariate polynomials over Z.

Author

Sasaki, Tateaki; Ookura, Yasutaka

Publisher

ACM Press

Published

2009

Language

EN