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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="ja" xml:id="balanc">

    <refnamediv>

        <refname>balanc</refname>

        <refpurpose>行列またはペンシルの平衡化</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[Ab,X]=balanc(A)

            [Eb,Ab,X,Y]=balanc(E,A)

        </synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A:  </term>

                <listitem>

                    <para>実数正方行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>X:  </term>

                <listitem>

                    <para>可逆な実数正方行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>E:  </term>

                <listitem>

                    <para>

                        実数正方行列 (<literal>A</literal>と同じ次元)

                    </para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Y:  </term>

                <listitem>

                    <para>可逆な実数正方行列.</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            正方行列の条件数を改善するために平衡化します.

        </para>

        <para>

            <literal>[Ab,X] = balanc(A)</literal> は,

            以下のような相似変換<literal>X</literal>を見つけます:

        </para>

        <para>

            <literal>Ab = inv(X)*A*X</literal>が近似的に等しい

            行ノルムおよび列ノルムを有する.

        </para>

        <para>

            行列ペンシルの場合,平衡化は一般化固有値問題を改善することにより

            行われます.

        </para>

        <para>

            <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> は,

            <literal>Eb=inv(X)*E*Y,  Ab=inv(X)*A*Y</literal> となるような

            左および右変換

            <literal>X</literal> および <literal>Y</literal> を返します.

        </para>

    </refsection>

    <refsection>

        <title>注意</title>

        <para>

            平衡化は関数<literal>bdiag</literal> および <literal>spec</literal>

            で行われます.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
A=[1/2^10,1/2^10;2^10,2^10];
[Ab,X]=balanc(A);
norm(A(1,:))/norm(A(2,:))
norm(Ab(1,:))/norm(Ab(2,:))
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="bdiag">bdiag</link>

            </member>

            <member>

                <link linkend="spec">spec</link>

            </member>

            <member>

                <link linkend="schur">schur</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

