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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>fr</LANGUAGE>
  <TITLE>sva  </TITLE>
  <TYPE>Scilab Function  </TYPE>
  <DATE>April 1993  </DATE>
  <SHORT_DESCRIPTION name="sva"> approximation de valeurs singulières  </SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
  <CALLING_SEQUENCE_ITEM>[U,s,V]=sva(A,k)  </CALLING_SEQUENCE_ITEM>
  <CALLING_SEQUENCE_ITEM>[U,s,V]=sva(A,tol)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
 <PARAM_INDENT>
  <PARAM_ITEM>
  <PARAM_NAME>A  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : matrice réelle ou complexe
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
  <PARAM_ITEM>
  <PARAM_NAME>k  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : entier
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
  <PARAM_ITEM>
  <PARAM_NAME>tol  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : nombre réel positif
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
 </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
  <P>
    Approximation de valeurs singulières.
  </P>
  <P>
    <VERB>[U,S,V]=sva(A,k)</VERB> avec <VERB>k</VERB> un entier
    &gt;=1, renvoie <VERB>U,S</VERB> et <VERB>V</VERB> telles que
    <VERB>B=U*S*V&apos;</VERB> est la meilleure approximation au sens
    l_2 de <VERB>A</VERB> avec rang(<VERB>B</VERB>)=<VERB>k</VERB>.
  </P>
  <P>
     <VERB>[U,S,V]=sva(A,tol)</VERB> où <VERB>tol</VERB> est un réel
    positif, renvoie <VERB>U,S</VERB> et <VERB>V</VERB> tels que
    <VERB>B=U*S*V&apos;</VERB> et la norme l_2 de <VERB>A-B</VERB> est
    inférieure à <VERB>tol</VERB>.
  </P>
  </DESCRIPTION>
  <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))
 ]]></EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM> <LINK>svd</LINK> </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
