<div class="wims_chemin">\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20" border=0>}\link{main}{Rsolution numrique de l'quation \( f ( x ) = 0 \)} <img src="gifs/arrows/right3.32.gif" alt=" ---> " width="25" height="15" border=0 valign="bottom"> \link{mainS3}{III  Mthode de point fixe} <img src="gifs/arrows/right3.32.gif" alt=" ---> " width="25" height="15" border=0 valign="bottom"> \link{mainS3S2}{III-2  Point attractif} <img src="gifs/arrows/right3.32.gif" alt=" ---> " width="25" height="15" border=0 valign="bottom"> III-2-3  Intervalle de convergence</div><table width=100%><tr><td valign=top><div class="left_toc"><p>
\link{mainS1}{I  Introduction}

\link{mainS2}{II  Mthode de dichotomie}

<div class="left_selection">\link{mainS3}{III  Mthode de point fixe}</div>

\link{mainS4}{IV  Mthode de Newton}

\link{mainS5}{V  Mthode de Lagrange}

\link{mainS6}{VI  Bibliographie}

\link{mainS7}{VII  Exercices}


\link{index}{Index}</div></td><td valign=top align=left width=100%><div class="wimsdoc">
<h2 class="thm">Proposition</h2><div class="thm">
En pratique, un intervalle de convergence \( V_{\alpha} \) peut tre calcul comme suit:
<ol><li>  Si \( 0 \leq g'(\alpha) < 1 \), prendre comme intervalle de convergence 
<div class="math">\(V_{\alpha} = \lbrack \beta, \; \gamma\rbrack \)</div> contenant \( \alpha \) 
tel que <div class="math">\(0 \leq g'(x) < 1, \; \forall x \in  \lbrack \beta, \; \gamma\rbrack  .\)</div> 
 </li><li>  Si \( -1 < g'(\alpha) < 0 \), prendre comme intervalle de convergence 
<div class="math">\(V_{\alpha} = \lbrack \beta, \; g(\beta)\rbrack \)</div>
tel que <div class="math">\(-1 < g'(x) < 0, \; \forall x \in  \lbrack \beta, \; g(\beta)\rbrack  .\)</div>
 </li></ol>
</div>




\fold{mainS3S2S3F_preu1}{<span class="preu">Preuve</span>

}</div></td><td valign=top align=right> <div class="right_toc">
\link{mainS3S2S1}{III-2-1  Thorme de convergence}

\link{mainS3S2S2}{III-2-2  Illustration graphique}

<div class="right_selection">\link{mainS3S2S3}{III-2-3  Intervalle de convergence}</div>
</div><center>\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20" border=0>}</center></td></tr></table>