Optimization and dynamical systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2014
|
| Edition: | [softcover repr. of hardcover ed. 1994] |
| Series: | Communications and control engineering
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 403 S. Ill., graph. Darst. 254 mm x 178 mm, 795 g |
| ISBN: | 9781447134695 1447134699 |
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MARC
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| 100 | 1 | |a Helmke, Uwe |d 1952-2016 |e Verfasser |0 (DE-588)172133122 |4 aut | |
| 245 | 1 | 0 | |a Optimization and dynamical systems |c Uwe Helmke and John B. Moore |
| 250 | |a [softcover repr. of hardcover ed. 1994] | ||
| 264 | 1 | |a London [u.a.] |b Springer |c 2014 | |
| 300 | |a XIII, 403 S. |b Ill., graph. Darst. |c 254 mm x 178 mm, 795 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Communications and control engineering | |
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| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 653 | |a Research | ||
| 653 | |a Dynamical System | ||
| 653 | |a Dynamische Systeme | ||
| 653 | |a Kontrolltheorie | ||
| 653 | |a Numerische Lineare Algebra | ||
| 653 | |a Optimisierung | ||
| 653 | |a Signalverarbeitung | ||
| 653 | |a control theory | ||
| 653 | |a dynamical systems | ||
| 653 | |a numerical linear algebra | ||
| 653 | |a optimization | ||
| 653 | |a signal processing | ||
| 689 | 0 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 1 | |a Optimierung |0 (DE-588)4043664-0 |D s |
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Record in the Search Index
| _version_ | 1806330381205504000 |
|---|---|
| adam_text |
Contents
Matrix
Eigenvalue Methods
і
1.1
Introduction
. 1
1.2
Power Method for Diagonalization
. 5
1.3
The Rayleigh Quotient Gradient Flow
. 14
1.4
The QR Algorithm
. 30
1.5
Singular Value Decomposition
(SVD)
. 35
1.6
Standard Least Squares Gradient Flows
. 38
Double Bracket
Isospectral
Flows
43
2.1
Double Bracket Flows for Diagonalization
. 43
2.2
Toda
Flows and the Riccati Equation
. 58
2.3
Recursive Lie-Bracket Based Diagonalization
. 68
Singular Value Decomposition
81
3.1
SVD
via Double Bracket Flows
. 81
3.2
A Gradient Flow Approach to
SVD
. 84
Linear Programming
3.01
4.1
The
Rôle
of Double Bracket Flows
. 103.
4.2
Interior Point Flows on a Polytope
.
AH
4.3
Recursive Linear Programming/Sorting
. 117
Approximation and Control
125
xii Contents
5.1
Approximations
by Lower Rank Matrices
. 125
5.2
The Polar Decomposition
. 143
5.3
Output Feedback Control
. 146
6
Balanced Matrix Factorizations
163
6Л
Introduction
. 163
6.2
Kempf-Ness Theorem
. 165
6.3
Global Analysis of Cost Functions
. 168
6.4
Flows for Balancing Transformations
. 172
6.5
Flows on the Factors X and
Y
. 186
6.6
Recursive Balancing Matrix Factorizations
. 193
7
Invariant Theory and System Balancing
201
7.1
Introduction
. 201
7.2
Plurisubharmonic Functions
. 204
7.3
The Azad-Loeb Theorem
. 207
7.4
Application to Balancing
. 209
7.5
Euclidean Norm Balancing
. 220
8
Balancing via Gradient Flows
229
8.1
Introduction
. 229
8.2
Flows on Positive Definite Matrices
. 231
8.3
Flows for Balancing Transformations
. 246
8.4
Balancing via Isodynamical Flows
. 249
8.5
Euclidean Norm Optimal Realizations
. 258
9
Sensitivity Optimization
269
9.1
A Sensitivity Minimizing Gradient Flow
. 269
9.2
Related L2-Sensitivity Minimization Flows
. 282
9.3
Recursive L2-Sensitivity Balancing
. 291
9.4
L2-Sensitivity Model Reduction
. 295
9.5
Sensitivity Minimization with Constraints
. 298
A Linear Algebra
311
A.I Matrices and Vectors
. 311
A.
2
Addition and Multiplication of Matrices
. 312
A.3 Determinant and Rank of a Matrix
. 312
A.4 Range Space, Kernel and Inverses
. 313
A.5 Powers, Polynomials, Exponentials and Logarithms
. 314
A.
6
Eigenvalues, Eigenvectors and Trace
. 314
A.7 Similar Matrices
. 315
A.8 Positive Definite Matrices and Matrix Decompositions
. . . 316
Contents xiii
Α.
9
Norms of Vectors and Matrices
. 317
A.
10 Kronecker
Product and
Vec
. 318
A.
11
Differentiation and Integration
. 318
A.
12
Lemma of Lyapunov
. 319
A.
13
Vector Spaces and Subspaces
. . 319
A.
14
Basis and Dimension
. 320
A.
15
Mappings and Linear Mappings
. 320
A.
16
Inner Products
. 321
Dynamical Systems
323
B.I Linear Dynamical Systems
. 323
B.2 Linear Dynamical System Matrix Equations
. 325
B.3 Controllability and Stabilizability
. 325
B.4 Observability and Detectability
. 326
B.5 Minimality
. 327
B.6 Markov Parameters and Hankel Matrix
. 327
B.7 Balanced Realizations
. 328
B.8 Vector Fields and Flows
. 329
B.9 Stability Concepts
. 330
B.10 Lyapunov Stability
. 332
Global Analysis
335
C.I Point Set Topology
. 335
C.2 Advanced Calculus
. 338
C.3 Smooth Manifolds
. 341
C.4 Spheres,
Projective
Spaces and Grassmannians
. 343
C.5 Tangent Spaces and Tangent Maps
. 346
C.6 Submanifolds
. 349
C.7 Groups, Lie Groups and Lie Algebras
. 351
C.8 Homogeneous Spaces
. 355
C.9 Tangent Bundle
. 357
C.10 Riemannian Metrics and Gradient Flows
. 360
C.ll Stable Manifolds
. 362
C.
12
Convergence of Gradient Flows
. 365
References S6T
Author Index
389
Subject Index
395 |
| any_adam_object | 1 |
| author | Helmke, Uwe 1952-2016 Moore, John B. 1941- |
| author_GND | (DE-588)172133122 (DE-588)129338648 |
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| author_role | aut aut |
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| bvnumber | BV042325214 |
| ctrlnum | (OCoLC)904010336 (DE-599)DNB1050174429 |
| discipline | Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | [softcover repr. of hardcover ed. 1994] |
| format | Book |
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| id | DE-604.BV042325214 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T02:08:10Z |
| institution | BVB |
| isbn | 9781447134695 1447134699 |
| language | English |
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| physical | XIII, 403 S. Ill., graph. Darst. 254 mm x 178 mm, 795 g |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series2 | Communications and control engineering |
| spelling | Helmke, Uwe 1952-2016 Verfasser (DE-588)172133122 aut Optimization and dynamical systems Uwe Helmke and John B. Moore [softcover repr. of hardcover ed. 1994] London [u.a.] Springer 2014 XIII, 403 S. Ill., graph. Darst. 254 mm x 178 mm, 795 g txt rdacontent n rdamedia nc rdacarrier Communications and control engineering Dynamisches System (DE-588)4013396-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Research Dynamical System Dynamische Systeme Kontrolltheorie Numerische Lineare Algebra Optimisierung Signalverarbeitung control theory dynamical systems numerical linear algebra optimization signal processing Dynamisches System (DE-588)4013396-5 s Optimierung (DE-588)4043664-0 s DE-604 Moore, John B. 1941- Verfasser (DE-588)129338648 aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4643699&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027762060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Helmke, Uwe 1952-2016 Moore, John B. 1941- Optimization and dynamical systems Dynamisches System (DE-588)4013396-5 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4043664-0 |
| title | Optimization and dynamical systems |
| title_auth | Optimization and dynamical systems |
| title_exact_search | Optimization and dynamical systems |
| title_full | Optimization and dynamical systems Uwe Helmke and John B. Moore |
| title_fullStr | Optimization and dynamical systems Uwe Helmke and John B. Moore |
| title_full_unstemmed | Optimization and dynamical systems Uwe Helmke and John B. Moore |
| title_short | Optimization and dynamical systems |
| title_sort | optimization and dynamical systems |
| topic | Dynamisches System (DE-588)4013396-5 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Dynamisches System Optimierung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4643699&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027762060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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