[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 ...
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 ...
[EN] In this paper, we propose, to the best of our knowledge, the first iterative scheme with memory for finding roots whose multiplicity is unknown existing in the literature. It improves the efficiency of a similar ...