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

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

Control Properties and Thermodynamic Analysis of Two Alternatives to Thermally Coupled Distillation Systems with Side Columns

The thermally coupled distillation configurations have received considerable attention because of their efficiency to reduce the energy required for the separation of ternary mixtures. The structure of the complex systems offers some control challenges arising from the transfer of vapor (or liquid) streams between the columns. Recently, some alternate schemes to thermally coupled distillation arrangements, that might provide better operational properties than the complex columns, have been proposed. In this work, we analyze the control properties of two alternative distillation schemes to the coupled systems. The theoretical control properties are analyzed with the application of the singular value decomposition technique. The results indicate that a reduction in the number of interconnections of the alternate configurations does not necessarily provide an improvement of its controllability properties. Also, second law calculations and energy consumptions were performed for the two alternate distillations schemes

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

Pré-Fabricaçao em edificios habitacionais a custos controlados

Hay una necesidad creciente para la construcción de viviendas, necesidad que se ha incrementado de forma exponencial en las últimas décadas. Esta necesidad es considerable en los países en vías de desarrollo, donde la población tiene una tasa de crecimiento elevada, mucho mayor que en los países desarrollados. Además, la población en el Mundo está desplazándose progresivamente hacia las ciudades. Es en los alrededores de las ciudades de países en desarrollo donde surge una necesidad de construir viviendas de coste controlado, asequibles, que se convierte en algunos casos en crítica. La Comisión de Prefabricación de la fib (International Federation for Structural Concrete, Federation Internationale du Béton, Federación Internacional del Hormigón Estructural) ha sido consciente por muchos años de este problema y tomó la decisión de crear un grupo de trabajo para desarrollar un documento sobre viviendas prefabricadas de coste asequible. Este documento estará dedicado a servir de ayuda sobre las técnicas de la prefabricación para las personas que deseen construir este tipo de viviendas. El presente artículo hace un resumen del trabajo desarrollado por este grupo hasta el momento

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