[EN] Finding a repeated zero for a nonlinear equation f(x) = 0, f : I subset of R -> R has always been of much interest and attention due to its wide applications in many fields of science and engineering. Modified Newton's ...
Amiri, Abdolreza; Darvishi, Mohammad Taghi; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2019-09)
[EN] In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we ...
Cordero Barbero, Alicia; Lotfi, T.; Khoshandi, A.; Torregrosa Sánchez, Juan Ramón(Société des Sciences Mathématiques de Roumanie, 2015)
[EN] Some methods with memory for solving nonlinear equations are designed from known methods without memory. We increase the convergence order from 4 to 6 by using a free parameter accelerator by Newton's interpolatory ...
A new two-parametric family of derivative-free iterative methods for solving nonlinear equations is presented. First, a new biparametric family without memory of optimal order four is proposed. The improvement of the ...
[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 ...
Candelario Villalona, Giro Guillermo; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, Maria P.(Elsevier, 2022-02)
[EN] In recent papers, some fractional Newton-type methods have been proposed by using the Riemann-Liouville and Caputo fractional derivatives in their iterative schemes, with order 2 alpha or 1+alpha. In this manuscript, ...
[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 ...
Ruiz Catalá, Carlos(Universitat Politècnica de València, 2015-10-29)
El método de Steffensen es un método iterativo para resolver ecuaciones no lineales basándose en aproximar la derivada en el método de Newton, lo que lo convierte en un método libre de derivadas. En este trabajo añadimos ...
Chicharro López, Francisco Israel(Universitat Politècnica de València, 2017-06-26)
Many problems in science, engineering or economy involve the search of the solution of an equation. Since ancient times, the modelling of nature problems has attracted a lot of interest, in order to predict the behaviour ...
García Maimo, Javier(Universitat Politècnica de València, 2017-11-28)
Since the appearance of Newton-Rapshon's method more than 300 years ago, iterative methods have become almost unassailable in most branches of science. The development of computing has made it possible to solve problems ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(John Wiley & Sons, 2020-01-12)
[EN] 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 ...
[EN] A parametric family of fourth-order schemes for computing the inverse and the Moore-Penrose inverse of a complex matrix is designed. A particular value of the parameter allows us to obtain a fifth-order method. ...
In this paper the problem of the determination of the preliminary orbit of a celestial body is studied. We compare the results obtained by the classical Gauss's method with those obtained by some higher-order iterative ...
Arroyo Martínez, Víctor; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Penkova Vassileva, María(Taylor & Francis Ltd, 2012)
In recent years, high-order methods have shown to be very useful in many practical applications, in which nonlinear systems arise. In this case, a classical method of positional astronomy have been modified in order to ...
Cordero Barbero, Alicia; Giménez-Palacios, Ivan; Torregrosa Sánchez, Juan Ramón(Elsevier, 2019-03)
[EN] Searching zeros of nonlinear functions often employs iterative procedures. In this paper, we construct several families of iterative methods with memory from one without memory, that is, we have increased the order ...
The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type ...