<?xml version="1.0" encoding="UTF-8"?>
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<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" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="nlev">
    <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 role="see also">
        <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>
</refentry>
