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

Petko D. Proinov

Applied Mathematics and Computation, 2016, vol. 284, issue C, 102-114

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).

Keywords: Simultaneous methods; Polynomial zeros; Semilocal convergence; Error estimates; Ehrlich method; Dochev–Byrnev method (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:284:y:2016:i:c:p:102-114

DOI: 10.1016/j.amc.2016.02.055

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