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Browsing by Subject "Order of convergence"

Now showing items 1-20 of 40

A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem

Andreu Estellés, Carlos; Cambil Teba, Noelia; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2014-04-01)

A derivative-free optimal eighth-order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences. Its performance, along with several ...
A class of Steffensen type methods with optimal order of convergente

Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2011-06-01)

In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided differences is used to get a ...
A family of modified Ostrowski's method with optimal eighth order of convergence

Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, María Penkova (Elsevier, 2011-12)

In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. Each iteration of these methods requires three evaluations of the function ...
A family of parametric schemes of arbitrary even order for solving nonlinear models

Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, Maria P. (Springer-Verlag, 2017)

[EN] Many problems related to gas dynamics, heat transfer or chemical reactions are modeled by means of partial differential equations that usually are solved by using approximation techniques. When they are transformed ...
A family of seventh-order schemes for solving nonlinear systems

Abad Rodríguez, Manuel Francisco; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Société des Sciences Mathématiques de Roumanie, 2014)

[EN] This paper focuses on solving nonlinear systems numerically. We propose an efficient family of three-step iterative schemes with seventh-order of convergence. The proposed methods are obtained by using the weight ...
A general class of arbitrary order iterative methods for computing generalized inverses

Cordero Barbero, Alicia; Soto-Quiros, Pablo; Torregrosa Sánchez, Juan Ramón (Elsevier, 2021-11-15)

[EN] A family of iterative schemes for approximating the inverse and generalized inverse of a complex matrix is designed, having arbitrary order of convergence p. For each p, a class of iterative schemes appears, for which ...
A general class of four parametric with and without memory iterative methods for nonlinear equations

Zafar, Fiza; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Rafi, Aneeqa (Springer-Verlag, 2019-05)

[EN] In this paper, we have constructed a derivative-free weighted eighth-order iterative class of methods with and without-memory for solving nonlinear equations. These methods are optimal as they satisfy Kung-Traub's ...
A highly efficient class of optimal fourth-order methods for solving nonlinear systems

Cordero Barbero, Alicia; Rojas-Hiciano, Renso V.; Torregrosa Sánchez, Juan Ramón; Vassileva, María P. (Springer-Verlag, 2024-04)

[EN] In this manuscript, we present a new class of highly efficient two-parameter optimal iterative methods for solving nonlinear systems that generalizes Ostrowski's method, King's Family, Chun's method, and KLAM Family ...
A new class of iterative processes for solving nonlinear systems by using one divided differences operator

Cordero Barbero, Alicia; Jordan-Lluch, Cristina; Sanabria-Codesal, Esther; Torregrosa Sánchez, Juan Ramón (MDPI AG, 2019-09)

[EN] In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that ...
A new efficient and optimal sixteenth-order scheme for simple roots of nonlinear equations

Behl, Ramandeep; Cordero Barbero, Alicia; Motsa, Sandile S.; Torregrosa Sánchez, Juan Ramón (2017)

[EN] In this manuscript, we propose a new highly efficient and optimal scheme of order sixteen for obtaining simple roots of nonlinear equations. The derivation of this scheme is based on the rational approximation approach. ...
A new efficient parametric family of iterative methods for solving nonlinear systems

Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón (Taylor & Francis, 2019-10-03)

[EN] A bi-parametric family of iterative schemes for solving nonlinear systems is presented. We prove for any value of parameters the sixth-order of convergence of any members of the class. The efficiency and computational ...
A new family of iterative methods widening areas of convergence

Budzko, Dzmitry; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2015-02-01)

[EN] A new parametric class of third-order iterative methods for solving nonlinear equations and systems is presented. These schemes are showed to be more stable than Newton’, Traub’ or Ostrowski’s procedures (in some ...
A New Third-Order Family of Multiple Root-Findings Based on Exponential Fitted Curve

Kanwar, Vinay; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Rajput, Mithil; Behl, Ramandeep (MDPI AG, 2023-03)

[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 ...
A new three-step class of iterative methods for solving nonlinear systems

Capdevila-Brown, Raudys Rafael; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (MDPI AG, 2019-12)

[EN] In this work, a new class of iterative methods for solving nonlinear equations is presented and also its extension for nonlinear systems of equations. This family is developed by using a scalar and matrix weight ...
An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry

Cordero Barbero, Alicia; Fiza Zafar; Ifra Ashraf; Torregrosa Sánchez, Juan Ramón (Springer-Verlag, 2023-01)

[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 ...
Approximation of artificial satellites' preliminary orbits: the efficiency challenge

Arroyo Martínez, Víctor; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2011-10)

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 ...
Artificial satellites preliminary orbit determination by the modified high-order Gauss method

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 ...
Derivative-free high-order methods applied to preliminary orbit determination

Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2013-04)

From position and velocity coordinates for several given instants, it is possible to determine the orbital elements of the preliminary orbit, taking only into account mutual gravitational attraction forces between the Earth ...
Domain of existence for the solution of some IVP's and BVP's by using an efficient ninth-order iterative method

Cevallos, Fabricio; Hueso, José L.; Martínez Molada, Eulalia; Howk, Cory L. (John Wiley & Sons, 2020-09-30)

[EN] In this paper, we consider the problem of solving initial value problems and boundary value problems through the point of view of its continuous form. It is well known that in most cases these types of problems are ...
Efficient high-order methods based on golden ratio for nonlinear system

Cordero Barbero, Alicia; Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2011-01-01)

We derive new iterative methods with order of convergence four or higher, for solving nonlinear systems, by composing iteratively golden ratio methods with a modified Newton's method. We use different efficiency indices ...