1 research outputs found
On a family of Weierstrass-type root-finding methods with accelerated convergence
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 , the th method of this family has the
order of convergence . 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.Comment: 18 pages, 5 tables, 2 figures. arXiv admin note: substantial text
overlap with arXiv:1508.0335