Abstract
This paper concerns the fast numerical factorization of degree a + b polynomials in a neighborhood of the polynomial x a . 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( dlog ϵ −1) 1+ δ floating point operations, with O(log ϵ −1) 1+ δ bits of precision. As far as complexity is concerned, this is the fastest algorithm known by the authors for that problem.
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