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A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously

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Abstract

In this paper, we first present a family of iterative algorithms for simultaneous determination of all zeros of a polynomial. This family contains two well-known algorithms: Dochev-Byrnev’s method and Ehrlich’s method. Second, using Proinov’s approach to studying convergence of iterative methods for polynomial zeros, we provide a semilocal convergence theorem that unifies the results of Proinov (Appl. Math. Comput. 284: 102–114, 2016) for Dochev-Byrnev’s and Ehrlich’s methods.

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  1. Faculty of Physics, University of Plovdiv, Plovdiv, 4000, Bulgaria

    Stoil I. Ivanov

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Ivanov, S.I. A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously. Numer Algor 75, 1193–1204 (2017). https://doi.org/10.1007/s11075-016-0237-1

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