<?xml version="1.0" encoding="UTF-8"?>

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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="glever">

    <refnamediv>

        <refname>glever</refname>

        <refpurpose>行列ペンシルの逆</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>E, A</term>

                <listitem>

                    <para>同じ次元の正方実行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>s</term>

                <listitem>

                    <para>

                        文字列 (デフォルト値 '<literal>s</literal>')

                    </para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Bfs,Bis</term>

                <listitem>

                    <para>多項式行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>chis</term>

                <listitem>

                    <para>多項式</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>一般化したLeverrierのアルゴリズムによりある行列ペンシルについて

        </para>

        <para>

            <literal>(s*E-A)^-1</literal>

        </para>

        <para>

            を計算します.

        </para>

        <programlisting role=""><![CDATA[
(s*E-A)^-1 = (Bfs/chis) - Bis.
 ]]></programlisting>

        <para>

            <literal>chis</literal> = 特性多項式 (乗法定数まで).

        </para>

        <para>

            <literal>Bfs</literal>  = 分子の特性多項式行列.

        </para>

        <para>

            <literal>Bis</literal>

            = 多項式行列 ( - <literal>(s*E-A)^-1</literal> の無限大までの級数展開).

        </para>

        <para>

            <literal>Bis</literal>の前に - 符号があることに注意してください.

        </para>

    </refsection>

    <refsection>

        <title>注意</title>

        <para>

            この関数は,<literal>Bfs,Bis</literal> および <literal>chis</literal>を

            簡単化するために <literal>cleanp</literal>を使用します.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1];
[Bfs,Bis,chis]=glever(F)
inv(F)-((Bfs/chis) - Bis)
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="rowshuff">rowshuff</link>

            </member>

            <member>

                <link linkend="det">det</link>

            </member>

            <member>

                <link linkend="invr">invr</link>

            </member>

            <member>

                <link linkend="coffg">coffg</link>

            </member>

            <member>

                <link linkend="pencan">pencan</link>

            </member>

            <member>

                <link linkend="penlaur">penlaur</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

