Listar por tema "basin of attraction"
Mostrando ítems 1-13 de 13
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Anomalies in the convergence of Traub-type methods with memory
(Blackwell Publishing Ltd, 2020)The stability analysis of a new family of iterative methods with memory is introduced. This family, designed from Traub's method, allows to add memory through the introduction of an accelerating parameter. Hence, the speed ... -
Anomalies in the convergence of Traub‐type methods with memory
(Computational and Mathematical Methods, 06/08/2019)The stability analysis of a new family of iterative methods with memory isintroduced. This family, designed from Traub's method, allows to add memorythrough the introduction of an accelerating parameter. Hence, the speed ... -
CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems
(Journal of Mathematical Chemistry, 03/2020)The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods ... -
Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
(MDPIMathematics, 11/10/2019)In this paper, using the idea of weight functions on the Potra–Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are ... -
Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability
(Axioms, 06/05/2019)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 ... -
Highly efficient family of iterative methods for solving nonlinear models
(Journal of Computational and Applied Mathematics, 15/01/2019)In this study, we present a new highly efficient sixth-order family of iterative methods for solving nonlinear equations along with convergence properties. Further, we extend this family to the multidimensional case ... -
On the choice of the best members of the Kim family and the improvement of its convergence
(Mathematical Methods in the Applied Sciences, 30/09/2020)The best members of the Kim family, in terms of stability, are obtained by using complex dynamics. From this elements, parametric iterative methods with memory are designed. A dynamical analysis of the methods with memory ... -
On the effect of the multidimensional weight functions on the stability of iterative processes
(Journal of Computational and Applied Mathematics, 15/05/2022)In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family ... -
Optimal Fourth-Order Weerakoon–Fernando-Type Methods for Multiple Roots and Their Dynamics
(Mediterranean Journal of Mathematics, 16/04/2019)In this paper, we present optimal fourth-order methods for finding multiple roots of non-linear equations, where the multiplicity is known in advance. These methods are based on the third-order method given by Weerakoon ... -
Stability and applicability of iterative methods with memory
(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 ... -
Stability study of eighth-order iterative methods for solving nonlinear equations
(Journal of Computational and Applied Mathematics, 01/2016)In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the ... -
Suitable approximations for the self-accelerating parameters in iterative methods with memory
(03/12/2020)Solving the nonlinear equation f(x)=0 is a common problem in several areas of Science and Engineering. Since exact solutions of the nonlinear equation are hardly available, scientists best rely on numerical solutions, such ... -
Third-degree anomalies of Traub's method
(Journal of Computational and Applied Mathematics, 01/2017)Traub’s method is a tough competitor of Newton’s scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be applied ...
