A fast and stable algorithm for splitting polynomials

This paper concerns the fast numerical factorization of degree a + b polynomials in a neighborhood of the polynomial xa. We want to obtain the so-called splitting of one such polynomial, i.e., a degree a factor with roots close to zero and a degree b factor with roots close to infinity. An important application of splitting is complete polynomial factorization or root finding. A new algorithm for splitting polynomials is presented. This algorithm requires O(dlogε−1)1+δ floating point operations, with O(logε−1)1+δ bits of precision. As far as complexity is concerned, this is the fastest algorithm known by the authors for that problem.