Abstract
LetS be a triangulation of ℂ andf(z) = z d +a d−1 z d−1+⋯+a 0, a complex polynomial. LetF be the piecewise linear approximation off determined byS. For certainS, we establish an upper bound on the complexity of an algorithm which finds zeros ofF. This bound is a polynomial in terms ofn, max{∥a i ∥} i , and measures of the sizes of simplices inS.
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Renegar, J. On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials. Mathematical Programming 32, 301–318 (1985). https://doi.org/10.1007/BF01582051
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DOI: https://doi.org/10.1007/BF01582051