1b1a69939f763da2b7f06869f1ad9cc687789988
[scilab.git] / scilab / modules / linear_algebra / help / ja_JP / eigen / projspec.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="projspec">
14     <refnamediv>
15         <refname>projspec</refname>
16         <refpurpose>スペクトル演算子</refpurpose>
17     </refnamediv>
18     <refsynopsisdiv>
19         <title>呼び出し手順</title>
20         <synopsis>[S,P,D,i]=projspec(A)</synopsis>
21     </refsynopsisdiv>
22     <refsection>
23         <title>パラメータ</title>
24         <variablelist>
25             <varlistentry>
26                 <term>A</term>
27                 <listitem>
28                     <para>正方行列</para>
29                 </listitem>
30             </varlistentry>
31             <varlistentry>
32                 <term>S, P, D</term>
33                 <listitem>
34                     <para>s正方行列</para>
35                 </listitem>
36             </varlistentry>
37             <varlistentry>
38                 <term>i</term>
39                 <listitem>
40                     <para>
41                         整数 (<literal>A</literal>のゼロ固有値の添字).
42                     </para>
43                 </listitem>
44             </varlistentry>
45         </variablelist>
46     </refsection>
47     <refsection>
48         <title>説明</title>
49         <para>
50             <literal>A</literal>の0におけるスペクトル特性.
51         </para>
52         <para>
53             <literal>S</literal> = 0における縮小レゾルベント 
54             (<literal>S</literal> = -Drazin_inverse(<literal>A</literal>)).
55         </para>
56         <para>
57             <literal>P</literal> = 0におけるスペクトル投影.
58         </para>
59         <para>
60             <literal>D</literal> = 0における冪零演算子.
61         </para>
62         <para>
63             <literal>index</literal> = 0固有値の添字.
64         </para>
65         <para>
66             特異点s=0の周りでの
67             <literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...</literal>
68             が出力されます.
69         </para>
70     </refsection>
71     <refsection>
72         <title>例</title>
73         <programlisting role="example"><![CDATA[ 
74 deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
75 A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
76 A=X*A*inv(X);
77 [S,P,D,index]=projspec(A);
78 index   //J-ブロックの大きさ
79 trace(P)  //J-ブロックの次元の合計
80 A*S-(eye()-P)
81 norm(D^index,1)
82  ]]></programlisting>
83     </refsection>
84     <refsection role="see also">
85         <title>参照</title>
86         <simplelist type="inline">
87             <member>
88                 <link linkend="coff">coff</link>
89             </member>
90         </simplelist>
91     </refsection>
92 </refentry>