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arXiv · 1508.04767

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

Petko D. Proinov·Maria T. Vasileva
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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 $N \ge 1$, the $N$th 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.

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Petko D. Proinov, Maria T. Vasileva. 2015-08-19. On a family of Weierstrass-type root-finding methods with accelerated convergence. https://arxiv.org/abs/1508.04767

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