Showing papers by "Alicia Cordero published in 2013"
TL;DR: In this paper, a complex dynamical analysis of the parametric fourth-order Kim's iterative family on quadratic polynomials is made, showing the MATLAB codes generated to draw the fractal images necessary to complete the study.
Abstract: The complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones).
147 citations
TL;DR: The analysis of the parameter space allows us to find elements of the King's family of iterative schemes for solving nonlinear equations that have bad convergence properties, and also other ones with stable behavior.
128 citations
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TL;DR: The complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study.
Abstract: In this paper the complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the Matlab codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated to the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us excellent schemes (or dreadful ones).
125 citations
TL;DR: The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials, and the property of immersion of the basins of attraction in all cases is analyzed.
103 citations
TL;DR: In this article, the dynamics of the Chebyshev-Halley family on quadratic polynomials is studied and a singular set, called cat set, appears in the parameter space associated to the family.
84 citations
TL;DR: The guest editors would like to express their gratitude to all those who submitted papers for publication and to the many reviewers whose reports were essential for us.
Abstract: The guest editors would like to express their gratitude to all those who submitted papers for publication and to the many reviewers whose reports were essential for us. We would also like to thank the editorial board members of this journal. Alicia Cordero and Juan R. Torregrosa were partially supported by Ministerio de Ciencia y Tecnologa MTM2011-28636-C02-02.
38 citations
TL;DR: A new technique to obtain derivative-free methods with optimal order of convergence in the sense of the Kung–Traub conjecture for solving nonlinear smooth equations is described, using Steffensen-like methods and Pade approximants.
35 citations
TL;DR: The application of the pseudocomposition technique on a set of multistep iterative methods for solving systems of nonlinear equations allows them to increase their order of convergence, obtaining new high-order, efficient methods.
32 citations
TL;DR: This work shows a general procedure to obtain optimal derivative free iterative methods (Kung and Traub (1974) for nonlinear equations f ( x ) = 0) by applying polynomial interpolation to a generic optimal derivativefree iterative method of lower order and applies this idea to Steffensen's method.
26 citations
TL;DR: In this paper, two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations, and numerical comparisons are made with other existing second-and fourth-order schemes to solve the nonlinear system of equations of the Global Positioning System and some academic non-linear systems.
Abstract: Two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations. Numerical comparisons are made with other existing second- and fourth-order schemes to solve the nonlinear system of equations of the Global Positioning System and some academic nonlinear systems.
25 citations
TL;DR: The classical King's family of fourth-order schemes is obtained as an special case and the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees are described.
Abstract: In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King's family of fourth-order schemes is obtained as an special case. We also present results for describing the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees.
TL;DR: The parameter space associated to the parametric family of Chebyshev-Halley on quadratic polynomials shows a dynamical richness worthy of study as discussed by the authors.
Abstract: The parameter space associated to the parametric family of Chebyshev-Halley on quadratic polynomials shows a dynamical richness worthy of study. This analysis has been initiated by the authors in previous works. Every value of the parameter belonging to the same connected component of the parameter space gives rise to similar dynamical behavior. In this paper, we focus on the search of regions in the parameter space that gives rise to the appearance of attractive orbits of period two.
TL;DR: In this paper, it is obtained that this family of Chebyshev–Halley schemes admits attractive 2-cycles in two different intervals, for real values of the parameter.
Abstract: The choice of a member of a parametric family of iterative methods is not always easy. The family of Chebyshev–Halley schemes is a good example of it. The analysis of bifurcation points of this family allows us to define a real interval in which there exist several problematic behaviours: attracting points that become doubled, other ones that become periodic orbits, etc. These aspects should be avoided in an iterative procedure, so it is important to determine the regions where this conduct takes place. In this paper, we obtain that this family admits attractive 2-cycles in two different intervals, for real values of the parameter.
TL;DR: In this article, a modified classical method for preliminary orbit determination is presented, where the spread of the observations is considerably wider than in the original method, as well as the order of convergence of the iterative scheme involved.
Abstract: A modified classical method for preliminary orbit
determination is presented. In our proposal, the spread of the
observations is considerably wider than in the original method, as
well as the order of convergence of the iterative scheme involved.
The numerical approach is made by using matricial weight functions,
which will lead us to a class of iterative methods with a sixth
local order of convergence. This is a process widely used in the
design of iterative methods for solving nonlinear scalar equations,
but rarely employed in vectorial cases. The numerical tests confirm
the theoretical results, and the analysis of the dynamics of the
problem shows the stability of the proposed schemes.
TL;DR: The method of iteration of the true anomaly is focused on, in which the secant method is replaced by more efficient methods, such as the second-order Steffensen’s method, as well as other high-order derivative-free methods.