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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>fr</LANGUAGE>
  <TITLE>nlev  </TITLE>
  <TYPE>Scilab Function  </TYPE>
  <DATE>April 1993  </DATE>
  <SHORT_DESCRIPTION name="nlev"> Algorithme de Leverrier   </SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[num,den]=nlev(A,z [,rmax])    </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
	<PARAM_NAME>A  </PARAM_NAME>
	<PARAM_DESCRIPTION>
	  <SP>
	    : matrice réelle carrée
	  </SP>
	</PARAM_DESCRIPTION> 
      </PARAM_ITEM>
      <PARAM_ITEM>
	<PARAM_NAME>z  </PARAM_NAME>
	<PARAM_DESCRIPTION>
	  <SP>
	    : chaîne de caractères
	  </SP>
	</PARAM_DESCRIPTION> 
      </PARAM_ITEM>
      <PARAM_ITEM>
	<PARAM_NAME>rmax  </PARAM_NAME>
	<PARAM_DESCRIPTION>
	  <SP>
	    : paramètre optionnel (voir <VERB>bdiag</VERB>) 
	  </SP>
	</PARAM_DESCRIPTION> 
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
      <VERB>[num,den]=nlev(A,z [,rmax])</VERB> calcule
      <VERB>(z*eye()-A)^(-1)</VERB> par bloc diagonalisation de
      <VERB>A</VERB> suivie de l&apos;algorithme de Leverrier sur chaque
      bloc.
    </P>
    <P>
    Cet algorithme est plus efficace que l&apos;algorithme de
    Leverrier seul, mais il n&apos;est toujours pas parfait !
    </P>
  </DESCRIPTION>
  <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))
    ]]></EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM> <LINK>coff</LINK> </SEE_ALSO_ITEM> 
    <SEE_ALSO_ITEM> <LINK>coffg</LINK> </SEE_ALSO_ITEM> 
    <SEE_ALSO_ITEM> <LINK>glever</LINK> </SEE_ALSO_ITEM> 
    <SEE_ALSO_ITEM> <LINK>ss2tf</LINK> </SEE_ALSO_ITEM>
  </SEE_ALSO>
  <AUTHORS>
    <AUTHORS_ITEM>
      F. Delebecque, INRIA; 
    </AUTHORS_ITEM>
    <AUTHORS_ITEM>
      S. Steer, INRIA;  
    </AUTHORS_ITEM>
  </AUTHORS>
</MAN>
