Optimization and dynamical systems:
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| Previous Title: | Optimization and dynamical systems |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Edition: | 3. print. |
| Series: | Communications and control engineering series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 367 - 387 |
| Physical Description: | XIII, 403 S. graph. Darst. |
| ISBN: | 3540198571 0387198571 |
Staff View
MARC
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| 001 | BV011182316 | ||
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| 008 | 970116s1996 gw d||| |||| 00||| ger d | ||
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| 084 | |a 27 |2 sdnb | ||
| 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 3. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a XIII, 403 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Communications and control engineering series | |
| 500 | |a Literaturverz. S. 367 - 387 | ||
| 650 | 4 | |a Dinámica diferenciable | |
| 650 | 4 | |a Optimización matemática | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Control theory | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 2 | 1 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Moore, John B. |d 1941- |e Verfasser |0 (DE-588)129338648 |4 aut | |
| 780 | 0 | 0 | |i Früher u.d.T. |t Optimization and dynamical systems |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007499005&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007499005 | |
Record in the Search Index
| _version_ | 1828141283753852928 |
|---|---|
| adam_text |
CONTENTS
1
MATRIX
EIGENVALUE
METHODS
1
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
2
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
3
SINGULAR
VALUE
DECOMPOSITION
81
3.1
SVD
VIA
DOUBLE
BRACKET
FLOWS
.
81
3.2
A
GRADIENT
FLOW
APPROACH
TO
SVD
.
84
4
LINEAR
PROGRAMMING
101
4.1
THE
ROLE
OF
DOUBLE
BRACKET
FLOWS
.
101
4.2
INTERIOR
POINT
FLOWS
ON
A
POLYTOPE
.
ILL
4.3
RECURSIVE
LINEAR
PROGRAMMING/SORTING
.
117
5
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
6.1
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
L
2
-SENSITIVITY
MINIMIZATION
FLOWS
.
282
9.3
RECURSIVE
L
2
-SENSITIVITY
BALANCING
.
291
9.4
L
2
-SENSITIVITY
MODEL
REDUCTION
.
295
9.5
SENSITIVITY
MINIMIZATION
WITH
CONSTRAINTS
.
298
A
LINEAR
ALGEBRA
311
A.L
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
A.9
NORMS
OF
VECTORS
AND
MATRICES
.
317
A.
10
KRONECKER
PRODUCT
AND
VEC
.
318
A.LL
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
B
DYNAMICAL
SYSTEMS
323
B.L
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
C
GLOBAL
ANALYSIS
335
C.L
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
367
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 |
| author_facet | Helmke, Uwe 1952-2016 Moore, John B. 1941- |
| author_role | aut aut |
| author_sort | Helmke, Uwe 1952-2016 |
| author_variant | u h uh j b m jb jbm |
| building | Verbundindex |
| bvnumber | BV011182316 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.5.H45 1994 |
| callnumber-search | QA402.5.H45 1994 |
| callnumber-sort | QA 3402.5 H45 41994 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 420 SK 780 SK 870 |
| ctrlnum | (OCoLC)258043432 (DE-599)BVBBV011182316 |
| dewey-full | 519.320 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 20 |
| dewey-search | 519.3 20 |
| dewey-sort | 3519.3 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. print. |
| format | Book |
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| id | DE-604.BV011182316 |
| illustrated | Illustrated |
| indexdate | 2025-03-31T20:03:08Z |
| institution | BVB |
| isbn | 3540198571 0387198571 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007499005 |
| oclc_num | 258043432 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-706 DE-521 DE-634 |
| owner_facet | DE-703 DE-20 DE-706 DE-521 DE-634 |
| physical | XIII, 403 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series2 | Communications and control engineering series |
| spelling | Helmke, Uwe 1952-2016 Verfasser (DE-588)172133122 aut Optimization and dynamical systems Uwe Helmke and John B. Moore 3. print. Berlin [u.a.] Springer 1996 XIII, 403 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Communications and control engineering series Literaturverz. S. 367 - 387 Dinámica diferenciable Optimización matemática Mathematical optimization Differentiable dynamical systems Control theory Dynamisches System (DE-588)4013396-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Dynamisches System (DE-588)4013396-5 s Moore, John B. 1941- Verfasser (DE-588)129338648 aut Früher u.d.T. Optimization and dynamical systems DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007499005&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Helmke, Uwe 1952-2016 Moore, John B. 1941- Optimization and dynamical systems Dinámica diferenciable Optimización matemática Mathematical optimization Differentiable dynamical systems Control theory 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_old | Optimization and dynamical systems |
| title_short | Optimization and dynamical systems |
| title_sort | optimization and dynamical systems |
| topic | Dinámica diferenciable Optimización matemática Mathematical optimization Differentiable dynamical systems Control theory Dynamisches System (DE-588)4013396-5 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Dinámica diferenciable Optimización matemática Mathematical optimization Differentiable dynamical systems Control theory Dynamisches System Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007499005&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT helmkeuwe optimizationanddynamicalsystems AT moorejohnb optimizationanddynamicalsystems |