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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="fr" xml:id="nlev">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>nlev</refname>
<refpurpose> Algorithme de Leverrier </refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Séquence d'appel</title>
<synopsis>[num,den]=nlev(A,z [,rmax])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Paramètres</title>
<variablelist>
<varlistentry>
<term>A </term>
<listitem>
<para>matrice réelle carrée
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>z </term>
<listitem>
<para>chaîne de caractères
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>rmax </term>
<listitem>
<para>paramètre optionnel (voir <literal>bdiag</literal>)
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para><literal>[num,den]=nlev(A,z [,rmax])</literal> calcule
<literal>(z*eye()-A)^(-1)</literal> par bloc diagonalisation de
<literal>A</literal> suivie de l'algorithme de Leverrier sur chaque
bloc.
</para>
<para>
Cet algorithme est plus efficace que l'algorithme de
Leverrier seul, mais il n'est toujours pas parfait !
</para>
</refsection>
<refsection>
<title>Exemples</title>
<programlisting role="example"><![CDATA[
A=rand(3,3);x=poly(0,'x');
[NUM,den]=nlev(A,'x')
clean(den-poly(A,'x'))
clean(NUM/den-inv(x*eye()-A))
]]></programlisting>
</refsection>
<refsection>
<title>Voir Aussi</title>
<simplelist type="inline">
<member>
<link linkend="coff">coff</link>
</member>
<member>
<link linkend="coffg">coffg</link>
</member>
<member>
<link linkend="glever">glever</link>
</member>
<member>
<link linkend="ss2tf">ss2tf</link>
</member>
</simplelist>
</refsection>
<refsection>
<title>Auteurs</title>
<simplelist type="vert">
<member>
F. Delebecque, INRIA;
</member>
<member>
S. Steer, INRIA;
</member>
</simplelist>
</refsection>
</refentry>
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