Loureiro, Ana F. and Cardoso, J. R. (2011) On the convergence of Schröder iteration functions for pth roots of complex numbers. Applied Mathematics and Computation, 217 (21). pp. 8833-8839. ISSN 0096-3003.
| The full text of this publication is not available from this repository. (Contact us about this Publication) | |
| Official URL http://dx.doi.org/10.1016/j.amc.2011.03.047 |
Abstract
In this work a condition on the starting values that guarantees the convergence of the Schröder iteration functions of any order to a pth root of a complex number is given. Convergence results are derived from the properties of the Taylor series coefficients of a certain function. The theory is illustrated by some computer generated plots of the basins of attraction.
| Item Type: | Article |
|---|---|
| Uncontrolled keywords: | Basins of attraction; Bell polynomials; Faà di Bruno’s formula; Iteration function; Order of convergence; pth root; Residuals; Taylor expansions |
| Subjects: | Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |
| Depositing User: | Ana F. Loureiro |
| Date Deposited: | 11 Oct 2012 15:02 |
| Last Modified: | 19 Feb 2013 12:34 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/31553 (The current URI for this page, for reference purposes) |
- Depositors only (login required):
