# J. R. Torregrosa

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- Publications
- Influence

Variants of Newton's Method using fifth-order quadrature formulas

- A. Cordero, J. R. Torregrosa
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 July 2007

Abstract Some variants of Newton’s method are developed in this work in order to solve nonlinear equations depending on one or several variables, based in rules of quadrature of fifth order. We prove… Expand

Steffensen type methods for solving nonlinear equations

- A. Cordero, J. Hueso, E. Martínez, J. R. Torregrosa
- Computer Science, Mathematics
- J. Comput. Appl. Math.
- 1 June 2012

In the present paper, by approximating the derivatives in the well known fourth-order Ostrowski's method and in a sixth-order improved Ostrowski's method by central-difference quotients, we obtain… Expand

A modified Newton-Jarratt’s composition

- A. Cordero, J. Hueso, E. Martínez, J. R. Torregrosa
- Mathematics, Computer Science
- Numerical Algorithms
- 1 September 2010

A reduced composition technique has been used on Newton and Jarratt’s methods in order to obtain an optimal relation between convergence order, functional evaluations and number of operations.… Expand

Variants of Newton's method for functions of several variables

- A. Cordero, J. R. Torregrosa
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 December 2006

Some variants of Newton's Method are developed in this work in order to solve systems of nonlinear equations, based in trapezoidal and midpoint rules of quadrature. We prove the quadratic convergence… Expand

Increasing the convergence order of an iterative method for nonlinear systems

- A. Cordero, J. Hueso, E. Martínez, J. R. Torregrosa
- Computer Science, Mathematics
- Appl. Math. Lett.
- 1 December 2012

Abstract In this work we introduce a technique for solving nonlinear systems that improves the order of convergence of any given iterative method which uses the Newton iteration as a predictor. The… Expand

Iterative methods of order four and five for systems of nonlinear equations

- A. Cordero, E. Martínez, J. R. Torregrosa
- Computer Science, Mathematics
- J. Comput. Appl. Math.
- 1 September 2009

The Adomian decomposition is used in order to obtain a family of methods to solve systems of nonlinear equations. The order of convergence of these methods is proved to be p>=2, under the same… Expand

Modified Newton's method for systems of nonlinear equations with singular Jacobian

- José L. Hueso, Eulalia Martínez, Juan R. Torregrosa
- Mathematics
- 1 February 2009

It is well known that Newton's method for a nonlinear system has quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. Here we present a modification of… Expand

Pseudocomposition: A technique to design predictor-corrector methods for systems of nonlinear equations

- A. Cordero, J. R. Torregrosa, María P. Vassileva
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 August 2012

Abstract A new technique for designing iterative methods for solving nonlinear systems is presented. This procedure, called pseudocomposition, uses a known method as a predictor and the Gaussian… Expand

Three-step iterative methods with optimal eighth-order convergence

- A. Cordero, J. R. Torregrosa, María P. Vassileva
- Computer Science, Mathematics
- J. Comput. Appl. Math.
- 1 March 2011

In this paper, based on Ostrowski's method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires… Expand

Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters

- Fiza Zafar, A. Cordero, R. Quratulain, J. R. Torregrosa
- Mathematics
- Journal of Mathematical Chemistry
- 1 August 2018

In this paper, we propose a family of optimal eighth order convergent iterative methods for multiple roots with known multiplicity with the introduction of two free parameters and three univariate… Expand