A family of Chebyshev-Halley type methods in Banach spaces

A family of third-order iterative processes (that includes Chebyshev and Halley's methods) is studied in Banach spaces. Results on convergence and uniqueness of solution are given, as well as error estimates. This study allows us to compare the most famous third-order iterative processes

Relaxing convergence conditions for an inverse-free Jarratt type approximation

We consider an inverse-free Jarratt-type approximation of order four in a Banach space (Argyros et al., 1996). We establish a convergence theorem by using recurrence relations. The purpose of this note is to relax convergence conditions and give an example where our convergence theorem can be applied but not the other ones

Discrete Sturm–Liouville problems, Jacobi matrices and Lagrange interpolation series

AbstractThe close relationship between discrete Sturm–Liouville problems belonging to the so-called limit-circle case, the indeterminate Hamburger moment problem and the search of self-adjoint extensions of the associated semi-infinite Jacobi matrix is well known. In this paper, all these important topics are also related with associated sampling expansions involving analytic Lagrange-type interpolation series

Increasing the applicability of Steffensen's method

We present an original alternative to the majorant principle of Kantorovich to study the semilocal convergence of Steffensen's method when it is applied to solve nonlinear systems which are differentiable. This alternative allows choosing starting points from which the convergence of Steffensen's method is guaranteed, but it is not from the majorant principle. Moreover, this study extends the applicability of Steffensen's method to the solution of nonlinear systems which are nondifferentiable and improves a previous result given by the authors. © 2014 Elsevier Inc. All rights reserved

On the correct choice of equivalent circuit for fitting bulk impedance data of ionic/electronic conductors

Bulk conductivity data of ionically and electronically conducting solid electrolytes and electronic ceramics invariably show a frequency dependence that cannot be modelled by a single-valued resistor. To model this, common practice is to add a constant phase element (CPE) in parallel with the bulk resistance. To fit experimental data on a wide variety of materials, however, it is also essential to include the limiting, high frequency permittivity of the material in the equivalent circuit. Failure to do so can lead to incorrect values for the sample resistance and CPE parameters and to an inappropriate circuit for materials that are electrically heterogeneous

Majorizing sequences for Newton’s method from initial value problems

AbstractThe most restrictive condition used by Kantorovich for proving the semilocal convergence of Newton’s method in Banach spaces is relaxed in this paper, providing we can guarantee the semilocal convergence in situations that Kantorovich cannot. To achieve this, we use Kantorovich’s technique based on majorizing sequences, but our majorizing sequences are obtained differently, by solving initial value problems

An extension of Gander’s result for quadratic equations

AbstractIn the study of iterative methods with high order of convergence, Gander provides a general expression for iterative methods with order of convergence at least three in the scalar case. Taking into account an extension of this result, we define a family of iterations in Banach spaces with R-order of convergence at least four for quadratic equations

A construction procedure of iterative methods with cubical convergence II: Another convergence approach

We extend the analysis of convergence of the iterations considered in Ezquerro et al. [Appl. Math. Comput. 85 (1997) 181] for solving nonlinear operator equations in Banach spaces. We establish a different Kantorovich-type convergence theorem for this family and give some error estimates in terms of a real parameter [-5, 1). © 1998 Elsevier Science Inc. All rights reserved

A note on a modification of Moser's method

We use a recurrence technique to obtain semilocal convergence results for Ulm's iterative method to approximate a solution of a nonlinear equation F (x) = 0fenced((x n + 1 = x n - B n F (x n),, n 0,; B n + 1 = 2 B n - B n F (x n + 1) B n,, n 0 .))This method does not contain inverse operators in its expression and we prove it converges with the Newton rate. We also use this method to approximate a solution of integral equations of Fredholm-type. © 2007 Elsevier Inc. All rights reserved

El control de los criterios de higiene de los procesos en mataderos de cerdo ibérico como medio para evaluar el funcionamiento aceptable de la producción

La normativa vigente obliga a los mataderos de cerdo ibérico a desarrollar e implantar un plan APPCC (Análisis de Peligros y Puntos de Control Crítico). De igual modo deben comprobar el correcto funcionamiento de su proceso de producción realizando controles microbiologícos de la superficie de las canales, siguiendo un plan de muestreo diseñado de acuerdo al Reglamento 2073/2005. En el presente trabajo se expone el diseño de un plan de muestreo de un matadero de cerdo ibérico, y se muestran los resultados obtenidos en los primeros controles realizados siguiendo dicho plan