On a family of Weierstrass-type root-finding methods with accelerated convergence

Petko D. Proinov and Maria T. Vasileva

Applied Mathematics and Computation, 2016, vol. 273, issue C, 957-968

Abstract: Kyurkchiev and Andreev (1985) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of this sequence of iterative methods is the famous method of Weierstrass (1891) and the second one is the method of Nourein (1977). For a given integer N ≥ 1, the Nth method of this family has the order of convergence N+1. Currently in the literature, there are only local convergence results for these methods. The main purpose of this paper is to present semilocal convergence results for the Weierstrass-type methods under computationally verifiable initial conditions and with computationally verifiable a posteriori error estimates.

Keywords: Simultaneous methods; Weierstrass method; Accelerated convergence; Local convergence; Semilocal convergence; Error estimates (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:273:y:2016:i:c:p:957-968

DOI: 10.1016/j.amc.2015.10.048

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