Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4626088 | Applied Mathematics and Computation | 2016 | 12 Pages |
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 N th method of this family has the order of convergence N+1N+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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Petko D. Proinov, Maria T. Vasileva,