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Résolution des systèmes linéaire par la méthode de gauss

exosup

11 déc., 2014

résolution des systèmes linéaire par la méthode de gauss

Université René Desca rtes

UFR de mathématiques et info rmatique

chapitre 1

Résolution des systèmes linéaires

Métho de de Gauss

Métho des numériques 2003/2004 - D.P astre

licence de mathématiques et licence MASS

Sommaire:

Résolution des systèmes linéaires

Notations

Etude des solutions

Théorie

Expression des solutions par la règle de Cramer :

Calcul théorique d’un déterminant

Méthode de Gauss

Exemple

Notation

Autre façon de conduire les calculs

Remarque + des exemples

Résolution

2 phases :

-éliminations → système triangulaire équivalent

- substitutions → résolution

itérations

Fin de la résolution

Notation matricielle

Algorithme

Premier programme Scilab

Meilleur Scilab

fonction Scilab

Recherche de pivot non nul

Calcul du déterminant

programme complet avec imp ressions intermédiaires et calcul du déterminant

Gauss 2ème version

Nouvel algorithme

Programmation

Variante

Exercice

Recherche du pivot maximal

Programme

Complexité

Retour sur la notation matricielle

Résolution des systèmes linéaires Méthode de Gauss s1

Télécharger

Nom du fichier : cours-gauss Résolution des systèmes linéaire par la méthode de gauss.pdf

Taille du fichier : 104 KB

Nombre de pages : 8

Date de publication : 11/12/2014

id=144

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