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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2006-2008 - 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 version="5.0-subset Scilab" xml:id="roots" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns5="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:db="http://docbook.org/ns/docbook">
<info>
<pubdate>$LastChangedDate: 2008-07-11 10:31:18 +0200 (ven., 11 juil. 2008)
$</pubdate>
</info>
<refnamediv>
<refname>roots</refname>
<refpurpose>roots of polynomials</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[x]=roots(p)
[x]=roots(p,'e')</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>p</term>
<listitem>
<para>polynomial with real or complex coefficients or vector of the
polynomial coefficients in decreasing degree order (Matlab
compatibility).</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para><literal>x=roots(p)</literal> returns in the complex vector
<literal>x</literal> the roots of the polynomial <literal>p</literal>. For
real polynomials of degree <=100 the fast RPOLY algorithm (based on
Jenkins-Traub method) is used. In the other cases the roots are computed
as the eigenvalues of the associated companion matrix. Use
<literal>x=roots(p,'e')</literal> to force this algorithm in any
cases.</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
p=poly([0,10,1+%i,1-%i],'x');
roots(p)
A=rand(3,3);roots(poly(A,'x')) // Evals by characteristic polynomial
spec(A)
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member><link linkend="poly">poly</link></member>
<member><link linkend="spec">spec</link></member>
<member><link linkend="companion">companion</link></member>
</simplelist>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Serge Steer (INRIA)</member>
</simplelist>
</refsection>
<refsection>
<title>References</title>
<para>The RPOLY algorithm is described in "Algorithm 493: Zeros of a Real
Polynomial", ACM TOMS Volume 1, Issue 2 (June 1975), pp. 178-189</para>
<para>Jenkins, M. A. and Traub, J. F. (1970), A Three-Stage Algorithm for
Real Polynomials Using Quadratic Iteration, SIAM J. Numer. Anal., 7(1970), 545-566.</para>
<para>Jenkins, M. A. and Traub, J. F. (1970), Principles for Testing Polynomial Zerofinding Programs.
ACM TOMS 1, 1 (March 1975), pp. 26-34</para>
</refsection>
<refsection>
<title>Used Functions</title>
<para>The rpoly.f source codes can be found in the directory
SCI/modules/polynomials/src/fortran of a Scilab source distribution. In the case where the
companion matrix is used, the eigenvalue computation is perfomed using
DGEEV and ZGEEV LAPACK codes.</para>
</refsection>
</refentry>
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