Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
New progress in real and complex polynomial root-finding
Computers & Mathematics with Applications
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A family of root-finding algorithms is constructed that combines knowledge of the branched covering structure of a polynomial with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that computes an $\epsilon$-factorization of a polynomial of degree $d$ that has an arithmetic complexity of $\Order{d(\log d)^2|\log\epsilon| +d^2(\log d)^2}$. At the present time, this complexity is the best known in terms of the degree.