King-Type Derivative-Free Iterative Families: Real and Memory Dynamics

A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stabilit...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2017-01, Vol.2017 (2017), p.1-15
Main Authors: Vassileva, María P., Torregrosa, Juan R., Cordero, Alicia, Chicharro, Francisco I.
Format: Article
Language:English
Subjects:
Analysis
Applied mathematics
Dynamical systems
Efficiency
Iterative methods
Iterative methods (Mathematics)
Methods
Nonlinear equations
Polynomials
Rational functions
Stability analysis
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Summary:A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.
ISSN:1076-2787
1099-0526
DOI:10.1155/2017/2713145