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On the convergence order of accelerated root iterations

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Summary

A Gauss-Seidel procedure for accelerating the convergence of the generalized method of the root iterations type of the (k+2)-th order (k∈N) for finding polynomial complex zeros, given in [7], is considered in this paper. It is shown that theR-order of convergence of the accelerated method is at leastk+1+σ n (k), where σ n (k)>1 is the unique positive root of the equation σn-σ-k-1 = 0 andn is the degree of the polynomial. The examples of algebraic equations in ordinary and circular arithmetic are given.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electronic Engineering, P.O. Box 73, YU-18000, Niš, Yugoslavia

    Miodrag Petković & Lidija Stefanović

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  1. Miodrag Petković
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  2. Lidija Stefanović
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Petković, M., Stefanović, L. On the convergence order of accelerated root iterations. Numer. Math. 44, 463–476 (1984). https://doi.org/10.1007/BF01405575

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  • DOI: https://doi.org/10.1007/BF01405575

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