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

Author

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  • Proinov, Petko D.
  • Vasileva, Maria T.

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.

Suggested Citation

  • Proinov, Petko D. & Vasileva, Maria T., 2016. "On a family of Weierstrass-type root-finding methods with accelerated convergence," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 957-968.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:957-968
    DOI: 10.1016/j.amc.2015.10.048
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    Cited by:

    1. Proinov, Petko D. & Ivanov, Stoil I. & Petković, Miodrag S., 2019. "On the convergence of Gander’s type family of iterative methods for simultaneous approximation of polynomial zeros," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 168-183.

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