Newton : recursos interactivos de Física : ESO y Bachillerato.

Resumen basado en el de la publicación

La manzana de la discordia : recuerdo de Newton.

Fruta excepcional la manzana tiene intervenciones destacadas en la historia y en la fábula de la humanidad. Ha dado apellidos variados, nombres geográficos insignes de todas las manzanas, no es la de Adán o Blacanieves la que nos interesa, sino la de Newton, de la discordia porque la mayoría de estudiantes no están de acuerdo en lo que pudo sugerir al gran científico y porque surgieron importantes conflictos, acerca de la prioridad de los descubrimientos. Todos los físicos reconocen que los cálculos de Newton y sus ideas han permitido la conquista de la luna entre otros descubrimientos. Lo importante es que su ley de la gravitación universal ha permitido los viajes interplanetarios no fue algo aislado, sino que forma parte de un todo que afectó a toda la Mecánica y como consecuencia a toda la Física. Interesa saber que no fue un creador de un par de leyes y ya está, fue un revolucionario, es el creador de la Física que hoy conocemos que no tiene nada que ver con la que en su tiempo se conocía. Lo importante de su descubrimiento es que queda encuadrado en un cuerpo general de doctrina, la Dinámica, que a la vez es fundamento de toda una doctrina general. La Mecánica Celeste, lo que fue ampliamente demostrado por el descubridor. Otro descubrimiento de Newton es que el cálculo ha entrado definitivamente en la Fisica.

Segunda Ley de Newton con un huevo que no se rompe.

El artículo forma parte de un monográfico dedicado a trabajos prácticos de investigación

Proyecto Newton : matem??ticas para la vida : una v??a para el apredizaje significativo de las matem??ticas

Resumen basado en el de la publicaci??n

A Newton method for pose refinement of 3D models

Different optimization methods can be employed to optimize a numerical estimate for the match between an instantiated object model and an image. In order to take advantage of gradient-based optimization methods, perspective inversion must be used in this context. We show that convergence can be very fast by extrapolating to maximum goodness-of-fit with Newton's method. This approach is related to methods which either maximize a similar goodness-of-fit measure without use of gradient information, or else minimize distances between projected model lines and image features. Newton's method combines the accuracy of the former approach with the speed of convergence of the latter.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

XMM-Newton temperature maps for five intermediate redshift clusters of galaxies

We have analyzed XMM-Newton archive data for five clusters of galaxies (redshifts 0.223-0.313) covering a wide range of dynamical states, from relaxed objects to clusters undergoing several mergers. We present here temperature maps of the X-ray gas together with a preliminary interpretation of the formation history of these clusters. (c) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Newton`s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton`s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.