<?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="sva">
    <refnamediv>
        <refname>sva</refname>
        <refpurpose>approximation de valeurs singulières  </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Séquence d'appel</title>
        <synopsis>[U,s,V]=sva(A,k)
            [U,s,V]=sva(A,tol)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Paramètres</title>
        <variablelist>
            <varlistentry>
                <term>A  </term>
                <listitem>
                    <para>matrice réelle ou complexe
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>k  </term>
                <listitem>
                    <para>entier
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol  </term>
                <listitem>
                    <para>nombre réel positif
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Approximation de valeurs singulières.
        </para>
        <para>
            <literal>[U,S,V]=sva(A,k)</literal> avec <literal>k</literal> un entier
            &gt;=1, renvoie <literal>U,S</literal> et <literal>V</literal> telles que
            <literal>B=U*S*V'</literal> est la meilleure approximation au sens
            l_2 de <literal>A</literal> avec rang(<literal>B</literal>)=<literal>k</literal>.
        </para>
        <para>
            <literal>[U,S,V]=sva(A,tol)</literal> où <literal>tol</literal> est un réel
            positif, renvoie <literal>U,S</literal> et <literal>V</literal> tels que
            <literal>B=U*S*V'</literal> et la norme l_2 de <literal>A-B</literal> est
            inférieure à <literal>tol</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Exemples</title>
        <programlisting role="example"><![CDATA[
A=rand(5,4)*rand(4,5);
[U,s,V]=sva(A,2);
B=U*s*V';
svd(A)
svd(B)
clean(svd(A-B))
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>Voir aussi</title>
        <simplelist type="inline">
            <member>
                <link linkend="svd">svd</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
