Loureiro, Ana F., 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. (doi:10.1016/j.amc.2011.03.047) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31553)
| The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |
| 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 |
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| DOI/Identification number: | 10.1016/j.amc.2011.03.047 |
| 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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
| Depositing User: | Ana F. Loureiro |
| Date Deposited: | 11 Oct 2012 15:02 UTC |
| Last Modified: | 05 Nov 2024 10:14 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/31553 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Loureiro, Ana F..
| Creator's ORCID: |
 https://orcid.org/0000-0002-4137-8822
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