Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability
Chicharro, Francisco Israel (1)
Torregrosa, Juan Ramón
Tipo de Ítem:article
In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing the sufficient conditions for the weight function. Many known schemes are members of this family for particular choices of the weight function. The dynamical behavior of one of these choices is presented, analyzing the stability of the fixed points and the critical points of the rational function obtained when the iterative expression is applied on low degree polynomials. Several numerical tests are given to compare different elements of the proposed family on non-polynomial problems.
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Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 15/03/2019)Based on the third-order Traub’s method, two iterative schemes with memory are introduced. The proper inclusion of accelerating parameters allows the introduction of memory. Therefore, the order of convergence of the ...
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