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Abstract
In this paper, the dynamics of the family of c-iterative methods for solving nonlinear equations are studied on quadratic polynomials. A singular parameter space is presented to show the complexity of the family. The analysis of the parameter space allows us to find elements of the family that have bad convergence properties and also other ones with very stable behaviour. These schemes correspond to values of c in different small regions of the parameter space.
Acknowledgements
The authors thank the anonymous referees for their valuable suggestions and comments.
Supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02. The first and fourth authors were also partially supported by P11B2011-30 (Universitat Jaume I), the second and third authors were also partially supported by Vicerrectorado de Investigación, Universitat Politècnica de València PAID-06-2010-2285.