On the convergence of Schröder iteration functions for pth roots of complex numbers

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)

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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)
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