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.
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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.
|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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