Search results for "convergence"

On the Convergence of Formal Integrals in Finite Time

1982

Consider a differential system: x = f (x) + e g(x), \(x \in {R^n}.\). Let h(x) = ho(x) + eh1 (x)... a “third” integral. For finite time t, I obtain an eo such that the series h(x) converges if e > eo. When t tends to infinite, eo tends to zero.

The beatles: tradition, avant-garde... and expressiveness

2019

Resumen: La música de The Beatles, tras su enorme éxito a través del tiempo, esconde diversos secretos que hunden sus raíces no solo en las tendencias coetáneas más evidentes -Pop Art, hippismo, cómic-, sino también en otras mucho más alejadas y sorprendentes que se refieren al manejo de las emociones, desde diversas herramientas armónicas procedentes de la música académica con la manifiesta influencia de las artes visuales, la pintura, la fotografía o la iconología sobre los álbumes del grupo. La continua búsqueda expresiva en The Beatles convirtió la música de la banda de Liverpool en una síntesis perfecta entre vanguardia y tradición a causa de la convergencia entre texto y sonido y, sob…

Approximation method for computationally expensive nonconvex multiobjective optimization problems

2012

Large Number Asymptotics for Two-Component Systems with Self-Consistent Coupling

2014

We shall consider the large number asymptotics of particle models for partial differential equations describing two component mixtures with simplest kind of self-consistent couplings. We shall recall in particular two examples related to different classes of models, the first one having both particle-like components and the second one having only one particle-like component (the other being described as a fluid); for these examples, different techniques on the probabilistic and analytic point of view are to be used to rigorously prove the convergence to a limit of the self-consistent terms in a “mean-field”-like asymptotics. The two models were analysed resp. in Bernardin and Ricci (Kinet R…

On superconvergence techniques

1987

A brief survey with a bibliography of superconvergence phenomena in finding a numerical solution of differential and integral equations is presented. A particular emphasis is laid on superconvergent schemes for elliptic problems in the plane employing the finite element method.

On the local and semilocal convergence of a parameterized multi-step Newton method

2020

Abstract This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-step iterative methods are computationally attractive.

Are near visual signs and symptoms in multiple sclerosis compatible with convergence insufficiency?

2021

Clinical relevance: Optometric management of neurodegenerative diseases is essential since visual signs, such as double vision, visual acuity reduction, or oculomotricity dysfunctions, are usually present in these subjects over the course of the disease. The present paper can guide clinicians in better managing their patients with multiple sclerosis. Background: Patients with multiple sclerosis present near vision symptoms that may be related to binocular anomalies, but these symptoms have not been investigated and related to specific signs. The aim of the present study was to evaluate the binocular vision in subjects with multiple sclerosis, and to analyse if the near visual signs and symp…

Variational Henstock integrability of Banach space valued functions

2016

We study the integrability of Banach space valued strongly measurable functions defined on $[0,1]$. In the case of functions $f$ given by $\sum \nolimits _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ are points of a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for Bochner and Pettis integrability of $f$. The function $f$ is Bochner integrable if and only if the series $\sum \nolimits _{n=1}^{\infty }x_n|E_n|$ is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of $f$. In this paper we give some conditions for variational Henstock integrability of a…

Growth and Spatial Dependence in Europe

2009

The convergence of European regions has been largely discussed in the empirical literature during the last decade. Two observations are often emphasized. First, the convergence rate among European regions appears to be very slow (Barro and Sala-i-Martins 1991, 1995; Armstrong 1995, Sala-i-Martin 1996a,b). Second, the tools used in the regional science literature show that the geographical distribution of European per capita GDP is highly clustered and characterized by global and local autocorrelation (Armstrong 1995; Ertur et al. 2007; Lopez-Bazo et al. 1999; Le Gallo and Ertur 2003 with a UE15 regional database and Ertur and Koch 2006, with a UE27 enlarged regional database). Many other st…

On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method

2017

The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. …