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A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich’s and Dochev–Byrnev’s methods

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  • Proinov, Petko D.

Abstract

In this paper, we establish a general semilocal convergence theorem (with computationally verifiable initial conditions and error estimates) for iterative methods for simultaneous approximation of polynomial zeros. As application of this theorem, we provide new semilocal convergence results for Ehrlich’s and Dochev–Byrnev’s root-finding methods. These results improve the results of Petković et al. (1998) and Proinov (2006). We also prove that Dochev–Byrnev’s method (1964) is identical to Prešić–Tanabe’s method (1972).

Suggested Citation

  • Proinov, Petko D., 2016. "A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich’s and Dochev–Byrnev’s methods," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 102-114.
    • Handle: RePEc:eee:apmaco:v:284:y:2016:i:c:p:102-114
    DOI: 10.1016/j.amc.2016.02.055
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    Cited by:

    1. Petko D. Proinov & Maria T. Vasileva, 2021. "A New Family of High-Order Ehrlich-Type Iterative Methods," Mathematics, MDPI, vol. 9(16), pages 1-25, August.

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