Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/9827
Title: | Point estimation of simultaneous methods for solving polynomial equations: A survey | Authors: | Petković, Milica Herceg D. |
Issue Date: | 1-Nov-2001 | Journal: | Journal of Computational and Applied Mathematics | Abstract: | One of the most important problems in solving nonlinear equations is the construction of such initial conditions which provide both the guaranteed and fast convergence of the considered numerical algorithm. Smale's approach from 1981, known as "point estimation theory", treats convergence conditions and the domain of convergence in solving an equation f(z) = 0 using only the information of f at the initial point z o . A procedure of this type is applied in this paper to iterative methods for the simultaneous approximation of simple zeros of polynomial equations. We have stated new, refined initial conditions which ensure the guaranteed convergence of the most frequently used simultaneous methods for solving algebraic equations: The Durand-Kerner method, Börsch-Supan method, the Ehrlich-Aberth method and the square-root family of one parameter methods. The stated initial conditions are of significant practical importance since they are computationally verifiable; they depend only on the coefficients of a given polynomial, its degree n and initial approximations to polynomial zeros. © 2001 Elsevier Science B.V. All rights reserved. | URI: | https://open.uns.ac.rs/handle/123456789/9827 | ISSN: | 3770427 | DOI: | 10.1016/S0377-0427(00)00620-8 |
Appears in Collections: | FTN Publikacije/Publications |
Show full item record
SCOPUSTM
Citations
29
checked on Nov 20, 2023
Page view(s)
33
Last Week
15
15
Last month
0
0
checked on May 10, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.