[EN] There are a good number of higher-order iterative methods for computing multiple zeros of nonlinear equations in the available literature. Most of them required first or higher-order derivatives of the involved function. ...
[EN] The aim of this paper is to introduce new high order iterative methods for multiple roots of the nonlinear scalar equation; this is a demanding task in the area of computational mathematics and numerical analysis. ...
[EN] In this paper, we present a new third-order family of iterative methods in order to compute the multiple roots of nonlinear equations when the multiplicity (m >= 1) is known in advance. There is a plethora of third-order ...
[EN] In this paper we revise the proofs of the results obtained in "Convergence radius of Osada's method under Holder continuous condition"[4], because the remainder of the Taylor's expansion used for the obtainment of the ...
Kansal, Munish; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Bhalla, Sonia(Walter de Gruyter GmbH, 2020-10)
[EN] There have appeared in the literature a lot of optimal eighth-order iterative methods for approximating simple zeros of nonlinear functions. Although, the similar ideas can be extended for the case of multiple zeros ...
[EN] In this paper we propose an alternative for the study of local convergence radius and the uniqueness radius for some third-order methods for multiple roots whose multiplicity is known. The main goal is to provide an ...
[EN] There is a very small number of higher-order iteration functions for multiple zeros whose order of convergence is greater than four. Some scholars have tried to propose optimal eighth-order methods for multiple zeros. ...
[EN] In this manuscript, we propose an iterative step that, combined with any other method, allows us to obtain an iterative scheme for approximating the simple roots of a polynomial simultaneously. We show that adding ...
[EN]
In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first order divided difference and weight functions. This iterative method is a three step ...
Zafar, Fiza; Cordero Barbero, Alicia; Rizvi, Dua-E-Zahra; Torregrosa Sánchez, Juan Ramón(American Institute of Mathematical Sciences, 2023)
[EN] The problem of solving a nonlinear equation is considered to be one of the significant domain. Motivated by the requirement to achieve more optimal derivative-free schemes, we present an eighth-order optimal derivative-free ...
[EN] There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance. Therefore, the principle focus of this paper is on developing a new fourth-order ...
[EN] In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the ...
[EN] The construction of derivative-free iterative methods for approximating multiple roots of a nonlinear equation is a relatively new line of research. This paper presents a novel family of one-parameter second-order ...
[EN] There is no doubt that the fourth-order King's family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, ...
[EN] In this work we focus on the problem of approximating multiple roots of nonlinear equations. Multiple roots appear in some applications such as the compression of band-limited signals and the multipactor effect in ...
Vázquez-Lozano, Juan Enrique; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2018)
[EN] In this paper, the performance of a parametric family including Newton¿s and Traub¿s schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well ...
[EN] The aim of this paper is the study of the robustness of classical methods defined for finding multiple roots with single multiplicity m when they are used for approximating different roots of a function having different ...
Mora Jiménez, María(Universitat Politècnica de València, 2019-07-30)
[ES] Existen problemas no lineales con soluciones de multiplicidad superior a 1. Ello nos obliga a utilizar técnicas iterativas adaptadas a este tipo de problemas y a diseñar
nuevas técnica que mejoren las ya existentes, ...
Triguero Navarro, Paula(Universitat Politècnica de València, 2023-06-16)
[ES] En gran cantidad de problemas de la matemática aplicada, existe la necesidad de resolver ecuaciones y sistemas no lineales, dado que numerosos problemas, finalmente, se reducen a estos. Conforme aumenta la dificultad ...
[EN] The main contribution of this study is to present a new optimal eighth-order scheme for locating zeros with multiplicity m > 1. An extensive convergence analysis is presented with the main theorem in order to demonstrate ...