Polynomial root-finding algorithms and branched covers

Details Polynomial root-finding algorithms and branched covers Polynomial root-finding algorithms and branched covers

1991-03-13

arxiv.org/abs/math/9201280v1

SIAM J. Comput. 23 No. 2 (1994), 415-436

Mathematics

Dynamical Systems

Scientific paper

10.1137/S0097539791201587

We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that computes an $\epsilon$-factorization of the polynomial which has an arithmetic complexity of $\Order{d^2(\log d)^2 + d(\log d)^2|\log\epsilon|}$. At the present time (1993), this complexity is the best known in terms of the degree.

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