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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="sva">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<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
>=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>
<title>Voir Aussi</title>
<simplelist type="inline">
<member>
<link linkend="svd">svd</link>
</member>
</simplelist>
</refsection>
</refentry>
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