Implementation of a Near-Optimal Complex Root Clustering Algorithm
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We describe Ccluster, a software for computing natural ϵ-clusters of complex roots in a given box of the complex plane. This algorithm from Becker et al. (2016) is near-optimal when applied to the benchmark problem of isolating all complex roots of an integer polynomial. It is one of the first implementations (Irina Voiculescu informed us that her student Dan-Andrei Gheorghe has independently implemented the same algorithm in a Masters Thesis Project (May 18, 2017) at Oxford University. Sewon Park and Martin Ziegler at KAIST, Korea, have implemented a modified version of Becker et al.(2016) for polynomials having only real roots being the eigenvalues of symmetric square matrices with real coefficients) of a near-optimal algorithm for complex roots. We describe some low level techniques for speeding up the algorithm. Its performance is compared with the well-known MPSolve library and Maple.
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