Méthode de dichotomie

Résumé

La méthode de dichotomie ou méthode de la bissection est, en mathématiques, un algorithme de recherche d'un zéro d'une fonction qui consiste à répéter des partages d’un intervalle en deux parties puis à sélectionner le sous-intervalle dans lequel existe un zéro de la fonction. Principe On considère deux nombres réels a et b et une fonction réelle f continue sur l'intervalle [a, b] telle que f(a) et f(b) soient de signes opposés. Supposons que nous voulions résoudre l'équation f(x) = 0. D'après le théorème des valeurs intermédiaires, f a au moins un zéro dans l’intervalle [a, b]. La méthode de dichotomie consiste à diviser l’intervalle en deux en calculant m = (''a''+''b'')/2. Il y a maintenant deux possibilités : soit f(a) et f(m) sont de signes contraires, soit f(m) et f(b) sont de signes contraires. L’algorithme de dichotomie est alors appliqué au sous-intervalle dans lequel le changement de signe se produ

Source officielle

https://fr.wikipedia.org/wiki/M%C3%A9thode_de_dichotomie

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Analysis of Rainfall Data by Simple Good Sense: is Spatial Statistics Worth the Trouble ?

Reinhard Furrer

This paper discusses the use of simple good sense in the spatial prediction of rainfall measurements in Switzerland. The method consists of a forecast based on the values of the available observations combined with topographic knowledge of the Swiss territory. Comparison of our subjective estimates with the true measurements is completed and yields surprisingly good results.

1998

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Structuration of micro-fluidic devices based on low temperature co-fired ceramic (LTCC) technology

Hansu Birol, Giancarlo Corradini, Yannick Fournier, Caroline Jacq, Thomas Maeder, Peter Ryser, Sigfrid Straessler

Smart packaging concept has been the driving force for the search of advanced technologies to produce multi-functional micro-scale devices for long years. In this sense, LTCC technology has been recently addressed as the suitable choice for a wide range of applications. In addition to its attractive characteristics for high-frequency applications those have been profited for a long time, it receives a growing attention for sensor applications in the recent years as well. This is due to the easy machinability of the LTCC tapes, which permits realization of complex structures such as membranes, channels, making it a suitable environment for micro-fluidic devices. These devices require utilization of supporting layers in order to prevent defects, often observed in forms of sagging, warpage or curling. The methods for elimination of these defects vary from passive precautions taken during lamination and firing to more elaborate methods such as use of sacrificial layers. The basic idea in the latter method is the preparation of a support, which can then be removed, leaving behind the desired structure. Among a number of alternatives, this paper focuses on and proposes the carbon-black sacrificial paste as an effective and simple method to fabricate membranes. Additionally determination of the open porosity elimination temperature in LTCC and effect of processing parameters on the fabricated structures, will be discussed. The methods of analysis will be TGA (thermo gravimetric analysis), dilatometer and SEM (scanning electron microscopy) analysis.

2005

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This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on a parameter. Specifically, we consider the situation when the parameter dependence is sufficiently smooth, and the aim is to compute solutions for many different parameter samples. On the basis of existing results for Lyapunov equations and parameter-dependent linear systems, we prove that the tensor containing all solution samples typically allows for an excellent low multilinear rank approximation. Stacking all sampled equations into one huge linear system, this fact can be exploited by combining the preconditioned CG method with low-rank truncation. Our approach is flexible enough to allow for a variety of preconditioners based, for example, on the sign function iteration or the alternating direction implicit method. © 2013 John Wiley & Sons, Ltd.

Wiley-Blackwell2013

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