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  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/cacsd/help/ja_JP/linmeq.xml
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<?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" version="5.0-subset Scilab" xml:lang="ja" xml:id="linmeq">
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  <refnamediv>
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    <refname>linmeq</refname>
5
 
    <refpurpose>シルベスタおよびリアプノフ方程式ソルバー</refpurpose>
6
 
  </refnamediv>
7
 
  <refsynopsisdiv>
8
 
    <title>呼び出し手順</title>
9
 
    <synopsis>[X(,sep)] = linmeq(task,A,(B,)C,flag,trans(,schur))</synopsis>
10
 
  </refsynopsisdiv>
11
 
  <refsection>
12
 
    <title>パラメータ</title>
13
 
    <variablelist>
14
 
      <varlistentry>
15
 
        <term>task</term>
16
 
        <listitem>
17
 
          <para>方程式の型を定義する整数オプション:</para>
18
 
          <variablelist>
19
 
            <varlistentry>
20
 
              <term>=1</term>
21
 
              <listitem>
22
 
                <para> シルベスタ方程式(1a) または (1b)を解きます ;</para>
23
 
              </listitem>
24
 
            </varlistentry>
25
 
            <varlistentry>
26
 
              <term>=2</term>
27
 
              <listitem>
28
 
                <para> リアプノフ方程式(2a) または (2b)を解きます;</para>
29
 
              </listitem>
30
 
            </varlistentry>
31
 
            <varlistentry>
32
 
              <term>=3</term>
33
 
              <listitem>
34
 
                <para>コレスキー分解 op(X) リアプノフ方程式 (3a) または (3b)を解きます.</para>
35
 
              </listitem>
36
 
            </varlistentry>
37
 
          </variablelist>
38
 
        </listitem>
39
 
      </varlistentry>
40
 
      <varlistentry>
41
 
        <term>A</term>
42
 
        <listitem>
43
 
          <para>実数行列</para>
44
 
        </listitem>
45
 
      </varlistentry>
46
 
      <varlistentry>
47
 
        <term>B</term>
48
 
        <listitem>
49
 
          <para>実数行列</para>
50
 
        </listitem>
51
 
      </varlistentry>
52
 
      <varlistentry>
53
 
        <term>C</term>
54
 
        <listitem>
55
 
          <para>実数行列</para>
56
 
        </listitem>
57
 
      </varlistentry>
58
 
      <varlistentry>
59
 
        <term>flag</term>
60
 
        <listitem>
61
 
          <para>(オプション) オプションを含む長さ3または2の整数ベクトル.</para>
62
 
          <variablelist>
63
 
            <varlistentry>
64
 
              <term>task</term>
65
 
              <listitem>
66
 
                <para>= 1 : flag の長さは3です</para>
67
 
                <variablelist>
68
 
                  <varlistentry>
69
 
                    <term>flag(1)</term>
70
 
                    <listitem>
71
 
                      <para>= 0 : 連続時間方程式 (1a)を解きます; そうでない場合, 
72
 
                        離散時間方程式 (1b)を解きます.
73
 
                      </para>
74
 
                    </listitem>
75
 
                  </varlistentry>
76
 
                  <varlistentry>
77
 
                    <term>flag(2)  </term>
78
 
                    <listitem>
79
 
                      <para>= 1 : A は (準) 上三角行列です;</para>
80
 
                    </listitem>
81
 
                  </varlistentry>
82
 
                  <varlistentry>
83
 
                    <term>flag(2)  </term>
84
 
                    <listitem>
85
 
                      <para>= 2 : A は上ヘッセンベルグ行列です;</para>
86
 
                    </listitem>
87
 
                  </varlistentry>
88
 
                  <varlistentry>
89
 
                    <term>それ以外</term>
90
 
                    <listitem>
91
 
                      <para>A は一般形式です.</para>
92
 
                    </listitem>
93
 
                  </varlistentry>
94
 
                  <varlistentry>
95
 
                    <term>flag(3)  </term>
96
 
                    <listitem>
97
 
                      <para>= 1 : B は準上三角行列です;</para>
98
 
                    </listitem>
99
 
                  </varlistentry>
100
 
                  <varlistentry>
101
 
                    <term>flag(3)  </term>
102
 
                    <listitem>
103
 
                      <para>= 2 : B は上ヘッセンベルグ行列です;</para>
104
 
                    </listitem>
105
 
                  </varlistentry>
106
 
                  <varlistentry>
107
 
                    <term>それ以外,  </term>
108
 
                    <listitem>
109
 
                      <para>B は一般形式です.</para>
110
 
                    </listitem>
111
 
                  </varlistentry>
112
 
                </variablelist>
113
 
              </listitem>
114
 
            </varlistentry>
115
 
            <varlistentry>
116
 
              <term>task</term>
117
 
              <listitem>
118
 
                <para>= 2 : flag の長さは2です</para>
119
 
                <variablelist>
120
 
                  <varlistentry>
121
 
                    <term>flag(1)</term>
122
 
                    <listitem>
123
 
                      <para>
124
 
                        0の場合, 連続時間方程式 (2a)を解きます; そうでない場合, 
125
 
                        離散時間方程式 (2b)を解きます.
126
 
                      </para>
127
 
                    </listitem>
128
 
                  </varlistentry>
129
 
                  <varlistentry>
130
 
                    <term>flag(2) </term>
131
 
                    <listitem>
132
 
                      <para>= 1 : A は (準) 上三角行列,　それ以外の場合,
133
 
                        A は一般形式です.
134
 
                      </para>
135
 
                    </listitem>
136
 
                  </varlistentry>
137
 
                </variablelist>
138
 
              </listitem>
139
 
            </varlistentry>
140
 
            <varlistentry>
141
 
              <term>task</term>
142
 
              <listitem>
143
 
                <para>= 3 : flag hの長さは2です</para>
144
 
                <variablelist>
145
 
                  <varlistentry>
146
 
                    <term>flag(1)  </term>
147
 
                    <listitem>
148
 
                      <para>= 0 : 
149
 
                        連続時間方程式 (3a)を解きます; そうでない場合, 
150
 
                        離散時間方程式 (3b)を解きます.
151
 
                      </para>
152
 
                    </listitem>
153
 
                  </varlistentry>
154
 
                  <varlistentry>
155
 
                    <term>flag(2)  </term>
156
 
                    <listitem>
157
 
                      <para>= 1 : 
158
 
                        A は (準) 上三角行列,　それ以外の場合,
159
 
                        A は一般形式です.
160
 
                      </para>
161
 
                    </listitem>
162
 
                  </varlistentry>
163
 
                </variablelist>
164
 
              </listitem>
165
 
            </varlistentry>
166
 
          </variablelist>
167
 
          <para>
168
 
            デフォルト:    flag(1) = 0, flag(2) = 0 (, flag(3) = 0).
169
 
          </para>
170
 
        </listitem>
171
 
      </varlistentry>
172
 
      <varlistentry>
173
 
        <term>trans</term>
174
 
        <listitem>
175
 
          <para>(オプション) 転置オプションを指定する整数.</para>
176
 
          <variablelist>
177
 
            <varlistentry>
178
 
              <term>=  </term>
179
 
              <listitem>
180
 
                <para>0 : op(M) = Mとして方程式 (1) - (3) を解きます.</para>
181
 
              </listitem>
182
 
            </varlistentry>
183
 
            <varlistentry>
184
 
              <term>=  </term>
185
 
              <listitem>
186
 
                <para>1 : op(M) = M' として方程式 (1) - (3) を解きます.</para>
187
 
              </listitem>
188
 
            </varlistentry>
189
 
            <varlistentry>
190
 
              <term>=  </term>
191
 
              <listitem>
192
 
                <para>2 : op(A) = A';  op(B) = B; として方程式 (1) を解きます.</para>
193
 
              </listitem>
194
 
            </varlistentry>
195
 
            <varlistentry>
196
 
              <term>=  </term>
197
 
              <listitem>
198
 
                <para>3 : op(A) = A;  op(B) = B'; として方程式 (1) を解きます.</para>
199
 
              </listitem>
200
 
            </varlistentry>
201
 
          </variablelist>
202
 
          <para>
203
 
            デフォルト:    trans = 0.
204
 
          </para>
205
 
        </listitem>
206
 
      </varlistentry>
207
 
      <varlistentry>
208
 
        <term>schur</term>
209
 
        <listitem>
210
 
          <para>(オプション) 
211
 
            Hessenberg-Schur法またはSchur法のどちらを
212
 
            使用するかを指定する整数.
213
 
            task = 1 で使用可能.
214
 
          </para>
215
 
          <variablelist>
216
 
            <varlistentry>
217
 
              <term>= 1 : Hessenberg-Schur 法 </term>
218
 
              <listitem>
219
 
                <para>(1個の行列がSchur形式に縮減されます).</para>
220
 
              </listitem>
221
 
            </varlistentry>
222
 
            <varlistentry>
223
 
              <term>= 2 : Schur 法</term>
224
 
              <listitem>
225
 
                <para>(2個の行列がSchur形式に縮減されます).</para>
226
 
              </listitem>
227
 
            </varlistentry>
228
 
          </variablelist>
229
 
          <para>
230
 
            デフォルト:    schur = 1.
231
 
          </para>
232
 
        </listitem>
233
 
      </varlistentry>
234
 
      <varlistentry>
235
 
        <term>X</term>
236
 
        <listitem>
237
 
          <para/>
238
 
        </listitem>
239
 
      </varlistentry>
240
 
      <varlistentry>
241
 
        <term>sep</term>
242
 
        <listitem>
243
 
          <para>(オプション) 
244
 
            (2.a)の場合 Sep(op(A),-op(A)'),
245
 
            (2.b)の場合 Sepd(A,A') の推定器.
246
 
          </para>
247
 
        </listitem>
248
 
      </varlistentry>
249
 
    </variablelist>
250
 
  </refsection>
251
 
  <refsection>
252
 
    <title>説明</title>
253
 
    <para>
254
 
      linmeq  関数は,
255
 
      SLICOT ルーチンSB04MD, SB04ND, SB04PD, SB04QD, 
256
 
      SB04RD, SB03MD, および SB03ODを用いて
257
 
      シルベスターおよびリアプノフ方程式を解きます.
258
 
    </para>
259
 
    <programlisting role=""><![CDATA[ 
 
3
    <refnamediv>
 
4
        <refname>linmeq</refname>
 
5
        <refpurpose>シルベスタおよびリアプノフ方程式ソルバー</refpurpose>
 
6
    </refnamediv>
 
7
    <refsynopsisdiv>
 
8
        <title>呼び出し手順</title>
 
9
        <synopsis>[X(,sep)] = linmeq(task,A,(B,)C,flag,trans(,schur))</synopsis>
 
10
    </refsynopsisdiv>
 
11
    <refsection>
 
12
        <title>パラメータ</title>
 
13
        <variablelist>
 
14
            <varlistentry>
 
15
                <term>task</term>
 
16
                <listitem>
 
17
                    <para>方程式の型を定義する整数オプション:</para>
 
18
                    <variablelist>
 
19
                        <varlistentry>
 
20
                            <term>=1</term>
 
21
                            <listitem>
 
22
                                <para> シルベスタ方程式(1a) または (1b)を解きます ;</para>
 
23
                            </listitem>
 
24
                        </varlistentry>
 
25
                        <varlistentry>
 
26
                            <term>=2</term>
 
27
                            <listitem>
 
28
                                <para> リアプノフ方程式(2a) または (2b)を解きます;</para>
 
29
                            </listitem>
 
30
                        </varlistentry>
 
31
                        <varlistentry>
 
32
                            <term>=3</term>
 
33
                            <listitem>
 
34
                                <para>コレスキー分解 op(X) リアプノフ方程式 (3a) または (3b)を解きます.</para>
 
35
                            </listitem>
 
36
                        </varlistentry>
 
37
                    </variablelist>
 
38
                </listitem>
 
39
            </varlistentry>
 
40
            <varlistentry>
 
41
                <term>A</term>
 
42
                <listitem>
 
43
                    <para>実数行列</para>
 
44
                </listitem>
 
45
            </varlistentry>
 
46
            <varlistentry>
 
47
                <term>B</term>
 
48
                <listitem>
 
49
                    <para>実数行列</para>
 
50
                </listitem>
 
51
            </varlistentry>
 
52
            <varlistentry>
 
53
                <term>C</term>
 
54
                <listitem>
 
55
                    <para>実数行列</para>
 
56
                </listitem>
 
57
            </varlistentry>
 
58
            <varlistentry>
 
59
                <term>flag</term>
 
60
                <listitem>
 
61
                    <para>(オプション) オプションを含む長さ3または2の整数ベクトル.</para>
 
62
                    <variablelist>
 
63
                        <varlistentry>
 
64
                            <term>task</term>
 
65
                            <listitem>
 
66
                                <para>= 1 : flag の長さは3です</para>
 
67
                                <variablelist>
 
68
                                    <varlistentry>
 
69
                                        <term>flag(1)</term>
 
70
                                        <listitem>
 
71
                                            <para>= 0 : 連続時間方程式 (1a)を解きます; そうでない場合, 
 
72
                                                離散時間方程式 (1b)を解きます.
 
73
                                            </para>
 
74
                                        </listitem>
 
75
                                    </varlistentry>
 
76
                                    <varlistentry>
 
77
                                        <term>flag(2)  </term>
 
78
                                        <listitem>
 
79
                                            <para>= 1 : A は (準) 上三角行列です;</para>
 
80
                                        </listitem>
 
81
                                    </varlistentry>
 
82
                                    <varlistentry>
 
83
                                        <term>flag(2)  </term>
 
84
                                        <listitem>
 
85
                                            <para>= 2 : A は上ヘッセンベルグ行列です;</para>
 
86
                                        </listitem>
 
87
                                    </varlistentry>
 
88
                                    <varlistentry>
 
89
                                        <term>それ以外</term>
 
90
                                        <listitem>
 
91
                                            <para>A は一般形式です.</para>
 
92
                                        </listitem>
 
93
                                    </varlistentry>
 
94
                                    <varlistentry>
 
95
                                        <term>flag(3)  </term>
 
96
                                        <listitem>
 
97
                                            <para>= 1 : B は準上三角行列です;</para>
 
98
                                        </listitem>
 
99
                                    </varlistentry>
 
100
                                    <varlistentry>
 
101
                                        <term>flag(3)  </term>
 
102
                                        <listitem>
 
103
                                            <para>= 2 : B は上ヘッセンベルグ行列です;</para>
 
104
                                        </listitem>
 
105
                                    </varlistentry>
 
106
                                    <varlistentry>
 
107
                                        <term>それ以外,  </term>
 
108
                                        <listitem>
 
109
                                            <para>B は一般形式です.</para>
 
110
                                        </listitem>
 
111
                                    </varlistentry>
 
112
                                </variablelist>
 
113
                            </listitem>
 
114
                        </varlistentry>
 
115
                        <varlistentry>
 
116
                            <term>task</term>
 
117
                            <listitem>
 
118
                                <para>= 2 : flag の長さは2です</para>
 
119
                                <variablelist>
 
120
                                    <varlistentry>
 
121
                                        <term>flag(1)</term>
 
122
                                        <listitem>
 
123
                                            <para>
 
124
                                                0の場合, 連続時間方程式 (2a)を解きます; そうでない場合, 
 
125
                                                離散時間方程式 (2b)を解きます.
 
126
                                            </para>
 
127
                                        </listitem>
 
128
                                    </varlistentry>
 
129
                                    <varlistentry>
 
130
                                        <term>flag(2) </term>
 
131
                                        <listitem>
 
132
                                            <para>= 1 : A は (準) 上三角行列,　それ以外の場合,
 
133
                                                A は一般形式です.
 
134
                                            </para>
 
135
                                        </listitem>
 
136
                                    </varlistentry>
 
137
                                </variablelist>
 
138
                            </listitem>
 
139
                        </varlistentry>
 
140
                        <varlistentry>
 
141
                            <term>task</term>
 
142
                            <listitem>
 
143
                                <para>= 3 : flag hの長さは2です</para>
 
144
                                <variablelist>
 
145
                                    <varlistentry>
 
146
                                        <term>flag(1)  </term>
 
147
                                        <listitem>
 
148
                                            <para>= 0 : 
 
149
                                                連続時間方程式 (3a)を解きます; そうでない場合, 
 
150
                                                離散時間方程式 (3b)を解きます.
 
151
                                            </para>
 
152
                                        </listitem>
 
153
                                    </varlistentry>
 
154
                                    <varlistentry>
 
155
                                        <term>flag(2)  </term>
 
156
                                        <listitem>
 
157
                                            <para>= 1 : 
 
158
                                                A は (準) 上三角行列,　それ以外の場合,
 
159
                                                A は一般形式です.
 
160
                                            </para>
 
161
                                        </listitem>
 
162
                                    </varlistentry>
 
163
                                </variablelist>
 
164
                            </listitem>
 
165
                        </varlistentry>
 
166
                    </variablelist>
 
167
                    <para>
 
168
                        デフォルト:    flag(1) = 0, flag(2) = 0 (, flag(3) = 0).
 
169
                    </para>
 
170
                </listitem>
 
171
            </varlistentry>
 
172
            <varlistentry>
 
173
                <term>trans</term>
 
174
                <listitem>
 
175
                    <para>(オプション) 転置オプションを指定する整数.</para>
 
176
                    <variablelist>
 
177
                        <varlistentry>
 
178
                            <term>=  </term>
 
179
                            <listitem>
 
180
                                <para>0 : op(M) = Mとして方程式 (1) - (3) を解きます.</para>
 
181
                            </listitem>
 
182
                        </varlistentry>
 
183
                        <varlistentry>
 
184
                            <term>=  </term>
 
185
                            <listitem>
 
186
                                <para>1 : op(M) = M' として方程式 (1) - (3) を解きます.</para>
 
187
                            </listitem>
 
188
                        </varlistentry>
 
189
                        <varlistentry>
 
190
                            <term>=  </term>
 
191
                            <listitem>
 
192
                                <para>2 : op(A) = A';  op(B) = B; として方程式 (1) を解きます.</para>
 
193
                            </listitem>
 
194
                        </varlistentry>
 
195
                        <varlistentry>
 
196
                            <term>=  </term>
 
197
                            <listitem>
 
198
                                <para>3 : op(A) = A;  op(B) = B'; として方程式 (1) を解きます.</para>
 
199
                            </listitem>
 
200
                        </varlistentry>
 
201
                    </variablelist>
 
202
                    <para>
 
203
                        デフォルト:    trans = 0.
 
204
                    </para>
 
205
                </listitem>
 
206
            </varlistentry>
 
207
            <varlistentry>
 
208
                <term>schur</term>
 
209
                <listitem>
 
210
                    <para>(オプション) 
 
211
                        Hessenberg-Schur法またはSchur法のどちらを
 
212
                        使用するかを指定する整数.
 
213
                        task = 1 で使用可能.
 
214
                    </para>
 
215
                    <variablelist>
 
216
                        <varlistentry>
 
217
                            <term>= 1 : Hessenberg-Schur 法 </term>
 
218
                            <listitem>
 
219
                                <para>(1個の行列がSchur形式に縮減されます).</para>
 
220
                            </listitem>
 
221
                        </varlistentry>
 
222
                        <varlistentry>
 
223
                            <term>= 2 : Schur 法</term>
 
224
                            <listitem>
 
225
                                <para>(2個の行列がSchur形式に縮減されます).</para>
 
226
                            </listitem>
 
227
                        </varlistentry>
 
228
                    </variablelist>
 
229
                    <para>
 
230
                        デフォルト:    schur = 1.
 
231
                    </para>
 
232
                </listitem>
 
233
            </varlistentry>
 
234
            <varlistentry>
 
235
                <term>X</term>
 
236
                <listitem>
 
237
                    <para/>
 
238
                </listitem>
 
239
            </varlistentry>
 
240
            <varlistentry>
 
241
                <term>sep</term>
 
242
                <listitem>
 
243
                    <para>(オプション) 
 
244
                        (2.a)の場合 Sep(op(A),-op(A)'),
 
245
                        (2.b)の場合 Sepd(A,A') の推定器.
 
246
                    </para>
 
247
                </listitem>
 
248
            </varlistentry>
 
249
        </variablelist>
 
250
    </refsection>
 
251
    <refsection>
 
252
        <title>説明</title>
 
253
        <para>
 
254
            linmeq  関数は,
 
255
            SLICOT ルーチンSB04MD, SB04ND, SB04PD, SB04QD, 
 
256
            SB04RD, SB03MD, および SB03ODを用いて
 
257
            シルベスターおよびリアプノフ方程式を解きます.
 
258
        </para>
 
259
        <programlisting role=""><![CDATA[ 
260
260
    [X] = linmeq(1,A,B,C,flag,trans,schur)
261
261
[X,sep] = linmeq(2,A,C,flag,trans)
262
262
    [X] = linmeq(2,A,C,flag,trans)
263
263
    [X] = linmeq(3,A,C,flag,trans)
264
264
 ]]></programlisting>
265
 
    <para>
266
 
      linmeq は種々のシルベスタおよびリアプノフ行列方程式を解きます:
267
 
    </para>
268
 
    <programlisting role=""><![CDATA[
 
265
        <para>
 
266
            linmeq は種々のシルベスタおよびリアプノフ行列方程式を解きます:
 
267
        </para>
 
268
        <programlisting role=""><![CDATA[
269
269
op(A)*X + X*op(B) = C,                           (1a)
270
270
 
271
271
op(A)*X*op(B) + X = C,                           (1b)
280
280
op(A)'*(op(X)'*op(X))*op(A) - op(X)'*op(X) =
281
281
                            - op(C)'*op(C),      (3b)
282
282
 ]]></programlisting>
283
 
    <para>
284
 
      ただし op(M) = M, または M'です.
285
 
    </para>
286
 
  </refsection>
287
 
  <refsection>
288
 
    <title>コメント</title>
289
 
    <variablelist>
290
 
      <varlistentry>
291
 
        <term>1.</term>
292
 
        <listitem>
293
 
          <para> (1a) または (1b)の場合でschur = 1の時, 
294
 
            Hessenberg-Schur法が使用され,1個の行列は
295
 
            ヘッセンベルク形式,
296
 
            その他の1個の行列は実数Schur形式に縮減されます.
297
 
            その他の場合,
298
 
            行列は両方共実数Schur形式に縮減されます.
299
 
            1個または両方の行列がすでにSchur/Hessenberg形式に縮減されている場合,
300
 
            flag(2) およびflag(3)でこのことを指定することができます.
301
 
            一般的な行列の場合,Hessenberg-Schur法は
302
 
            Schur法よりもはるかに効率的です.
303
 
          </para>
304
 
        </listitem>
305
 
      </varlistentry>
306
 
      <varlistentry>
307
 
        <term>2.</term>
308
 
        <listitem>
309
 
          <para>方程式 (2a) または (2b)において, 行列 C は対称と仮定されます.</para>
310
 
        </listitem>
311
 
      </varlistentry>
312
 
      <varlistentry>
313
 
        <term>3.</term>
314
 
        <listitem>
315
 
          <para>方程式 (3a) または (3b)において, 行列 A はそれぞれ安定または
316
 
            収束性を有する必要があります.
317
 
          </para>
318
 
        </listitem>
319
 
      </varlistentry>
320
 
      <varlistentry>
321
 
        <term>4.</term>
322
 
        <listitem>
323
 
          <para>方程式 (3a) または (3b)の場合, 計算される行列 X は
324
 
            解のコレスキー分解です, すなわち, 実際の解は op(X)'*op(X), 
325
 
            ただし X は上三角行列です.
326
 
          </para>
327
 
        </listitem>
328
 
      </varlistentry>
329
 
    </variablelist>
330
 
  </refsection>
331
 
  <refsection>
332
 
    <title>履歴</title>
333
 
    <para>
334
 
      V. Sima, Katholieke Univ. Leuven, Belgium, May 1999, May, Sep. 2000. V. Sima, University of Bucharest, Romania, May 2000.
335
 
    </para>
336
 
  </refsection>
337
 
  <refsection>
338
 
    <title>例</title>
339
 
    <programlisting role="example"><![CDATA[ 
 
283
        <para>
 
284
            ただし op(M) = M, または M'です.
 
285
        </para>
 
286
    </refsection>
 
287
    <refsection>
 
288
        <title>コメント</title>
 
289
        <variablelist>
 
290
            <varlistentry>
 
291
                <term>1.</term>
 
292
                <listitem>
 
293
                    <para> (1a) または (1b)の場合でschur = 1の時, 
 
294
                        Hessenberg-Schur法が使用され,1個の行列は
 
295
                        ヘッセンベルク形式,
 
296
                        その他の1個の行列は実数Schur形式に縮減されます.
 
297
                        その他の場合,
 
298
                        行列は両方共実数Schur形式に縮減されます.
 
299
                        1個または両方の行列がすでにSchur/Hessenberg形式に縮減されている場合,
 
300
                        flag(2) およびflag(3)でこのことを指定することができます.
 
301
                        一般的な行列の場合,Hessenberg-Schur法は
 
302
                        Schur法よりもはるかに効率的です.
 
303
                    </para>
 
304
                </listitem>
 
305
            </varlistentry>
 
306
            <varlistentry>
 
307
                <term>2.</term>
 
308
                <listitem>
 
309
                    <para>方程式 (2a) または (2b)において, 行列 C は対称と仮定されます.</para>
 
310
                </listitem>
 
311
            </varlistentry>
 
312
            <varlistentry>
 
313
                <term>3.</term>
 
314
                <listitem>
 
315
                    <para>方程式 (3a) または (3b)において, 行列 A はそれぞれ安定または
 
316
                        収束性を有する必要があります.
 
317
                    </para>
 
318
                </listitem>
 
319
            </varlistentry>
 
320
            <varlistentry>
 
321
                <term>4.</term>
 
322
                <listitem>
 
323
                    <para>方程式 (3a) または (3b)の場合, 計算される行列 X は
 
324
                        解のコレスキー分解です, すなわち, 実際の解は op(X)'*op(X), 
 
325
                        ただし X は上三角行列です.
 
326
                    </para>
 
327
                </listitem>
 
328
            </varlistentry>
 
329
        </variablelist>
 
330
    </refsection>
 
331
    <refsection>
 
332
        <title>履歴</title>
 
333
        <para>
 
334
            V. Sima, Katholieke Univ. Leuven, Belgium, May 1999, May, Sep. 2000. V. Sima, University of Bucharest, Romania, May 2000.
 
335
        </para>
 
336
    </refsection>
 
337
    <refsection>
 
338
        <title>例</title>
 
339
        <programlisting role="example"><![CDATA[ 
340
340
//(1a)
341
341
n=40;m=30;
342
342
A=rand(n,n);C=rand(n,m);B=rand(m,m);
371
371
X=linmeq(3,A,C,[1 0]);
372
372
norm(A'*X'*X*A - X'*X +C'*C,1)
373
373
 ]]></programlisting>
374
 
  </refsection>
375
 
  <refsection role="see also">
376
 
    <title>参照</title>
377
 
    <simplelist type="inline">
378
 
      <member>
379
 
        <link linkend="sylv">sylv</link>
380
 
      </member>
381
 
      <member>
382
 
        <link linkend="lyap">lyap</link>
383
 
      </member>
384
 
    </simplelist>
385
 
  </refsection>
 
374
    </refsection>
 
375
    <refsection role="see also">
 
376
        <title>参照</title>
 
377
        <simplelist type="inline">
 
378
            <member>
 
379
                <link linkend="sylv">sylv</link>
 
380
            </member>
 
381
            <member>
 
382
                <link linkend="lyap">lyap</link>
 
383
            </member>
 
384
        </simplelist>
 
385
    </refsection>
386
386
</refentry>