
A NearOptimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration
We describe a subdivision algorithm for isolating the complex roots of a...
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Polynomial root clustering and explicit deflation
We seek complex roots of a univariate polynomial P with real or complex ...
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Efficiently Computing Real Roots of Sparse Polynomials
We propose an efficient algorithm to compute the real roots of a sparse ...
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Implementation of a NearOptimal Complex Root Clustering Algorithm
We describe Ccluster, a software for computing natural ϵclusters of com...
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Root Radii and Subdivision for Polynomial RootFinding
The recent subdivision algorithms for univariate polynomial Complex Root...
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The Dplus Discriminant and Complexity of Root Clustering
Let p(x) be an integer polynomial with m≥ 2 distinct roots ρ_1,…,ρ_m who...
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Computing Real Roots of Real Polynomials ... and now For Real!
Very recent work introduces an asymptotically fast subdivision algorithm...
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Complexity Analysis of Root Clustering for a Complex Polynomial
Let F(z) be an arbitrary complex polynomial. We introduce the local root clustering problem, to compute a set of natural εclusters of roots of F(z) in some box region B_0 in the complex plane. This may be viewed as an extension of the classical root isolation problem. Our contribution is twofold: we provide an efficient certified subdivision algorithm for this problem, and we provide a bitcomplexity analysis based on the local geometry of the root clusters. Our computational model assumes that arbitrarily good approximations of the coefficients of F are provided by means of an oracle at the cost of reading the coefficients. Our algorithmic techniques come from a companion paper (Becker et al., 2018) and are based on the Pellet test, Graeffe and Newton iterations, and are independent of Schönhage's splitting circle method. Our algorithm is relatively simple and promises to be efficient in practice.
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