e6788771f581fb63db13725cc1dc87ea195168f4
[scilab.git] / scilab / modules / linear_algebra / help / ja_JP / eigen / balanc.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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13 <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">
14     <refnamediv>
15         <refname>balanc</refname>
16         <refpurpose>行列またはペンシルの平衡化</refpurpose>
17     </refnamediv>
18     <refsynopsisdiv>
19         <title>呼び出し手順</title>
20         <synopsis>[Ab,X]=balanc(A)
21             [Eb,Ab,X,Y]=balanc(E,A)
22         </synopsis>
23     </refsynopsisdiv>
24     <refsection>
25         <title>パラメータ</title>
26         <variablelist>
27             <varlistentry>
28                 <term>A:  </term>
29                 <listitem>
30                     <para>実数正方行列</para>
31                 </listitem>
32             </varlistentry>
33             <varlistentry>
34                 <term>X:  </term>
35                 <listitem>
36                     <para>可逆な実数正方行列</para>
37                 </listitem>
38             </varlistentry>
39             <varlistentry>
40                 <term>E:  </term>
41                 <listitem>
42                     <para>
43                         実数正方行列 (<literal>A</literal>と同じ次元)
44                     </para>
45                 </listitem>
46             </varlistentry>
47             <varlistentry>
48                 <term>Y:  </term>
49                 <listitem>
50                     <para>可逆な実数正方行列.</para>
51                 </listitem>
52             </varlistentry>
53         </variablelist>
54     </refsection>
55     <refsection>
56         <title>説明</title>
57         <para>
58             正方行列の条件数を改善するために平衡化します.
59         </para>
60         <para>
61             <literal>[Ab,X] = balanc(A)</literal> は,
62             <literal>Ab = inv(X)*A*X</literal>が近似的に等しい
63             行ノルムおよび列ノルムを有する
64             相似変換<literal>X</literal>を見つけます.
65         </para>
66         <para>
67             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
68             行われます.
69         </para>
70         <para>
71             <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> は,
72             <literal>Eb=inv(X)*E*Y,  Ab=inv(X)*A*Y</literal> となるような
73             左および右変換
74             <literal>X</literal> および <literal>Y</literal> を返します.
75         </para>
76     </refsection>
77     <refsection>
78         <title>注意</title>
79         <para>
80             平衡化は関数<literal>bdiag</literal> および <literal>spec</literal>
81             で行われます.
82         </para>
83     </refsection>
84     <refsection>
85         <title>例</title>
86         <programlisting role="example"><![CDATA[ 
87 A=[1/2^10,1/2^10;2^10,2^10];
88 [Ab,X]=balanc(A);
89 norm(A(1,:))/norm(A(2,:))
90 norm(Ab(1,:))/norm(Ab(2,:))
91  ]]></programlisting>
92     </refsection>
93     <refsection role="see also">
94         <title>参照</title>
95         <simplelist type="inline">
96             <member>
97                 <link linkend="bdiag">bdiag</link>
98             </member>
99             <member>
100                 <link linkend="spec">spec</link>
101             </member>
102             <member>
103                 <link linkend="schur">schur</link>
104             </member>
105         </simplelist>
106     </refsection>
107 </refentry>