forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathpower_method.html
264 lines (230 loc) · 6.7 KB
/
power_method.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
<html>
<head>
<title>
POWER_METHOD - The Power Method for Eigenvalues and Eigenvectors
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
POWER_METHOD <br> The Power Method for Eigenvalues and Eigenvectors
</h1>
<hr>
<p>
<b>POWER_METHOD</b>
is a C++ library which
carries out the power method.
</p>
<p>
The power method seeks to determine the eigenvalue of maximum modulus,
and a corresponding eigenvector.
</p>
<p>
The basic power method will not perform as expected if, corresponding to the
maximum modulus, there are complex eigenvalues, or a pair of real eigenvalues
of opposite sign. The power method's behavior can break down or be very
slow initially if the starting vector has a zero or very small component
in the eigenspace corresponding to the maximal eigenvalue.
</p>
<p>
A second version of the power method is included which can handle the case
of complex eigenvalues.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>POWER_METHOD</b> is available in
<a href = "../../c_src/power_method/power_method.html">a C version</a> and
<a href = "../../cpp_src/power_method/power_method.html">a C++ version</a> and
<a href = "../../f77_src/power_method/power_method.html">a FORTRAN77 version</a> and
<a href = "../../f_src/power_method/power_method.html">a FORTRAN90 version</a> and
<a href = "../../m_src/power_method/power_method.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/arpack/arpack.html">
ARPACK</a>,
a FORTRAN90 library which
computes eigenvalues for large matrices;
</p>
<p>
<a href = "../../f77_src/eispack/eispack.html">
EISPACK</a>,
a FORTRAN77 library which
carries out eigenvalue computations;
superseded by <a href = "../../f77_src/lapack/lapack.html">LAPACK</a>;
</p>
<p>
<a href = "../../cpp_src/test_eigen/test_eigen.html">
TEST_EIGEN</a>,
a C++ library which
implements test matrices for eigenvalue analysis.
</p>
<p>
<a href = "../../cpp_src/test_mat/test_mat.html">
TEST_MAT</a>,
a C++ library which
defines test matrices.
</p>
<p>
<a href = "../../f77_src/toms343/toms343.html">
TOMS343</a>,
a FORTRAN77 library which
computes the eigenvalues and
eigenvectors of a general real matrix;<br>
this is a FORTRAN77 version of ACM TOMS algorithm 343.
</p>
<p>
<a href = "../../f77_src/toms384/toms384.html">
TOMS384</a>,
a FORTRAN77 library which
computes the eigenvalues and eigenvectors
of a symmetric matrix;<br>
this is a FORTRAN77 version of ACM TOMS algorithm 384.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Richard Burden, Douglas Faires,<br>
Numerical Analysis,<br>
Thomson Brooks/Cole, 2004,<br>
ISBN13: 978-0534392000,<br>
LC: QA297.B84.
</li>
<li>
Ward Cheney, David Kincaid,<br>
Numerical Mathematics and Computing,<br>
Brooks-Cole Publishing, 2004,<br>
ISBN: 0534201121,<br>
LC: QA297.C426.
</li>
<li>
Gene Golub, Charles VanLoan,<br>
Matrix Computations,
Third Edition,<br>
Johns Hopkins, 1996,<br>
ISBN: 0-8018-4513-X,<br>
LC: QA188.G65.
</li>
<li>
Eric VanDeVelde,<br>
Concurrent Scientific Programming,<br>
Springer, 1994,<br>
ISBN: 0-387-94195-9,<br>
LC: QA76.58.V35.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "power_method.cpp">power_method.cpp</a>,
the source code.
</li>
<li>
<a href = "power_method.hpp">power_method.hpp</a>,
the include file.
</li>
<li>
<a href = "power_method.sh">power_method.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "power_method_prb.cpp">power_method_prb.cpp</a>, the tests;
</li>
<li>
<a href = "power_method_prb.sh">power_method_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "power_method_prb_output.txt">power_method_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CPU_TIME</b> reports the elapsed CPU time.
</li>
<li>
<b>FIBONACCI2</b> returns the FIBONACCI2 matrix.
</li>
<li>
<b>POWER_METHOD</b> applies several steps of the power method.
</li>
<li>
<b>POWER_METHOD2</b> applies the power method for possibly complex eigenvalues.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_EPSILON</b> returns the R8 roundoff unit.
</li>
<li>
<b>R8MAT_MV</b> multiplies a matrix times a vector.
</li>
<li>
<b>R8VEC_COPY</b> copies an R8VEC.
</li>
<li>
<b>R8VEC_DIVIDE</b> divides an R8VEC by a nonzero scalar.
</li>
<li>
<b>R8VEC_DOT</b> computes the dot product of a pair of R8VEC's.
</li>
<li>
<b>R8VEC_NORM_L2</b> returns the L2 norm of an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIS</b> returns the TRIS matrix.
</li>
<li>
<b>TRIS_EIGENVALUES</b> returns the eigenvalues of the TRIS matrix.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last modified on 28 May 2008.
</i>
<!-- John Burkardt -->
</body>
</html>