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Safe convergence of simultaneous methods for polynomial zeros

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Abstract

The theory of point estimation treating the initial conditions for the safe convergence of iterative processes for the simultaneous determination of polynomial zeros is considered. A general approach which makes use of corrections appearing in iterative formulas is given and demonstrated in the case of three well known methods without derivatives and based on Weierstrass’ corrections. The established convergence conditions are of practical importance since they depend only on available data: coefficients of a polynomial and initial approximations to the zeros.

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Authors and Affiliations

  1. Faculty of Electronic Engineering, University of Niš, 18 000, Niš, Yugoslavia

    Miodrag S. Petković & Snežana Ilić

  2. Institute of Mathematics, University of Novi Sad, 21 000, Novi Sad, Yugoslavia

    Đorđe Herceg

Authors
  1. Miodrag S. Petković
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  2. Đorđe Herceg
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  3. Snežana Ilić
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Petković, M.S., Herceg, Đ. & Ilić, S. Safe convergence of simultaneous methods for polynomial zeros. Numerical Algorithms 17, 313–331 (1998). https://doi.org/10.1023/A:1016688508558

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