A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods
Numerical Analysis
2015-11-13 v1
Abstract
In this paper, we establish a general semilocal convergence theorem (with computationally verifiable initial conditions and error estimates) for iterative methods for simultaneous approximation of polynomial zeros. As application of this theorem, we provide new semilocal convergence results for Ehrlich's and Dochev-Byrnev's root-finding methods. These results improve the results of Petkovi\'c, Herceg and Ili\'c [Numer. Algorithms 17 (1998) 313--331] and Proinov [C.~R. Acad. Bulg. Sci. 59 (2006) 705--712]. We also prove that Dochev-Byrnev's method (1964) is identical to Pre{\v s}i\'c-Tanabe's method (1972).
Keywords
Cite
@article{arxiv.1511.03821,
title = {A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods},
author = {Petko D. Proinov},
journal= {arXiv preprint arXiv:1511.03821},
year = {2015}
}
Comments
19 pages