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Journal of Complex Analysis
Volume 2018 (2018), Article ID 7289092, 11 pages
https://doi.org/10.1155/2018/7289092
Research Article

Fixed Point and Newton’s Methods in the Complex Plane

Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, 2500 Boul. de l’Université, Sherbrooke, QC, Canada J1K 2R1

Correspondence should be addressed to Calvin Gnang

Received 29 August 2017; Accepted 12 December 2017; Published 29 January 2018

Academic Editor: Daniel Girela

Copyright © 2018 François Dubeau and Calvin Gnang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We revisit the necessary and sufficient conditions for linear and high order of convergence of fixed point and Newton’s methods in the complex plane. Schröder’s processes of the first and second kind are revisited and extended. Examples and numerical experiments are included.