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Communications of the ACM

Communications of the ACM

A highly parallel algorithm for approximating all zeros of a polynomial with only real zeros

An algorithm is described based on Newton's method which simultaneously approximates all zeros of a polynomial with only real zeros. The algorithm, which is conceptually suitable for parallel computation, determines its own starting values so that convergence to the zeros is guaranteed. Multiple zeros and their multiplicity are readily determined. At no point in the method is polynomial deflation used.

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