Newtonian nonlinear dynamics for complex linear and optimization problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2013
|
| Schriftenreihe: | Nonlinear systems and complexity
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 135-136) and index |
| Beschreibung: | XII, 138 S. graph. Darst. 24 cm |
| ISBN: | 9781461459118 1461459117 |
Internformat
MARC
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|---|---|---|---|
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| 005 | 20131010 | ||
| 007 | t | ||
| 008 | 130913s2013 xxud||| |||| 00||| eng d | ||
| 010 | |a 2012951341 | ||
| 020 | |a 9781461459118 |c alk. paper |9 978-1-461-45911-8 | ||
| 020 | |a 1461459117 |c alk. paper |9 1-461-45911-7 | ||
| 035 | |a (OCoLC)828711274 | ||
| 035 | |a (DE-599)BVBBV041269967 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
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| 100 | 1 | |a Vázquez, Luis |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Newtonian nonlinear dynamics for complex linear and optimization problems |c Luis Vázquez, Salvador Jiménez |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2013 | |
| 300 | |a XII, 138 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Nonlinear systems and complexity |v 4 | |
| 500 | |a Includes bibliographical references (p. 135-136) and index | ||
| 650 | 4 | |a Nonlinear mechanics | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a System theory | |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Mechanik |0 (DE-588)4042095-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Systemtheorie |0 (DE-588)4058812-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Mechanik |0 (DE-588)4042095-4 |D s |
| 689 | 0 | 1 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 0 | 2 | |a Systemtheorie |0 (DE-588)4058812-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Jiménez, Salvador |e Sonstige |4 oth | |
| 830 | 0 | |a Nonlinear systems and complexity |v 4 |w (DE-604)BV041257000 |9 4 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026243596&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026243596 | ||
Datensatz im Suchindex
| _version_ | 1804150735318810624 |
|---|---|
| adam_text | Contents
1 Elements
of
Newtonian
Mechanics
......................................... 1
1.1
Introduction
.............................................................
I
1.2
One-Dimensional Motion of a Newtonian Particle
...................
I
1.3
One-Dimensional Motion with Linear Dissipation
.................... 4
1
.4
General Motion of a Particle in
q
Dimensions
......................... 5
1.4.1
Constant Gravitational Field
................................... 7
1.4.2
Quadratic Potential
............................................. 7
1
.5
Unconstrained
Extrema
................................................ 8
1.6
Exercises
.................................................................
II
2
Solution of Systems of IJnear Equations
.................................. 15
2.
1
introduction
............................................................. 15
2.2
GeneralCase
............................................................ 17
2.3
DampedMethod
........................................................ 19
2.4
Overdamped Method
.................................................... 23
2.5
Singular Matrix
.......................................................... 24
2.6
Exercises
................................................................. 25
3
Solution of Systems of Linear Equations: Numerical Simulations
..... 29
3.1
Comparison with Other Similar Methods
.....................,........ 29
3.1.1
Jacobi and Gauss-
Seidel
Methods
............................. 29
3.
1
.2
Steepest Descent Method
....................................... 30
3>.2 Choice of Parameter Values
............................................ 33
3.3
Singular Matrix
.......................................................... 38
3.4
Exercises
............................................-.................... 39
4
Eigenvalue Problems
............................. -.......................... 43
4.
í
Introduction
............................................................. 43
4.2
The Dynamical Systems
..................., —............. — ,.,.„., 44
4.2.
і
Main Properties
................ —.........................___ 44
4.2.2
Properties
oť
the Jacobian
...................................... 46
I
xii Contents
4.3
Proofs
.................................................................... 49
4.3.1
Spectrum of the Jacobian
....................................... 49
4.3.2
Stability
......................................................... 53
4.3.3
Complex Case
................................................... 57
4.4
Computation of Intermediate Eigenvalues of Matrices
................ 58
4.4.1
General Presentation
............................................ 58
4.4.2
Statement of the method
........................................ 61
4.5
Exercises
................................................................. 62
5
Eigenvalue Problems: Numerical Simulations
............................ 67
5.1
Introduction
............................................................. 67
5.2
The Dynamical System Method
........................................ 68
5.2.1
Some Examples in Three Dimensions
......................... 72
5.2.2
Comparison with the Power Methods
......................... 78
5.3
Intermediate Eigenvalues
............................................... 82
5.4
Enhancing the Convergence Rate
...................................... 83
5.4.1
A First Attempt
................................................. 84
5.4.2
A Better Choice
................................................. 84
5.4.3
An Alternative Quadratic Method
............................. 89
5.5
Exercises
................................................................. 96
6
Linear Programming
........................................................ 99
6.1
Introduction
............................................................. 99
6.2
Examples with One independent Variable
............................. 101
6.3
Examples with Two Independent Variables
............................ 102
6.4
General Problem with
q
Independent Variables
....................... 108
6.5
Challenges from the Mechanical Method
.............................. 112
6.6
Exercises
................................................................. 113
7
Quadratic Programming
.................................................... 117
7.1
Introduction
............................................................. 117
7.2
Quadratic Programming
................................................ 118
7.3
Quadratic Objective Function with Linear Constraints
............... 120
7.3.1
OneDimension
................................................. 120
7.3.2
Two Dimensions
................................................ 122
7.4
Linear Objective Function with Quadratic Constraints
...............
1
26
7.4.1
One Dimension
.................................................
1
26
7.4.2
Two Dimensions
................................................ 127
7.5
Extension to Nonlinear Programming
.................................. 128
7.6
Exercises
................................................................. 131
References
......................................................................... 135
Index
............................................................................... 137
|
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| ctrlnum | (OCoLC)828711274 (DE-599)BVBBV041269967 |
| dewey-full | 531.01/515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.01/515 |
| dewey-search | 531.01/515 |
| dewey-sort | 3531.01 3515 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV041269967 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:43:39Z |
| institution | BVB |
| isbn | 9781461459118 1461459117 |
| language | English |
| lccn | 2012951341 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026243596 |
| oclc_num | 828711274 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XII, 138 S. graph. Darst. 24 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Nonlinear systems and complexity |
| series2 | Nonlinear systems and complexity |
| spelling | Vázquez, Luis Verfasser aut Newtonian nonlinear dynamics for complex linear and optimization problems Luis Vázquez, Salvador Jiménez New York, NY [u.a.] Springer 2013 XII, 138 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Nonlinear systems and complexity 4 Includes bibliographical references (p. 135-136) and index Nonlinear mechanics Mathematical optimization System theory Optimierung (DE-588)4043664-0 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Systemtheorie (DE-588)4058812-9 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 s Optimierung (DE-588)4043664-0 s Systemtheorie (DE-588)4058812-9 s DE-604 Jiménez, Salvador Sonstige oth Nonlinear systems and complexity 4 (DE-604)BV041257000 4 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026243596&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vázquez, Luis Newtonian nonlinear dynamics for complex linear and optimization problems Nonlinear systems and complexity Nonlinear mechanics Mathematical optimization System theory Optimierung (DE-588)4043664-0 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Systemtheorie (DE-588)4058812-9 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4042095-4 (DE-588)4058812-9 |
| title | Newtonian nonlinear dynamics for complex linear and optimization problems |
| title_auth | Newtonian nonlinear dynamics for complex linear and optimization problems |
| title_exact_search | Newtonian nonlinear dynamics for complex linear and optimization problems |
| title_full | Newtonian nonlinear dynamics for complex linear and optimization problems Luis Vázquez, Salvador Jiménez |
| title_fullStr | Newtonian nonlinear dynamics for complex linear and optimization problems Luis Vázquez, Salvador Jiménez |
| title_full_unstemmed | Newtonian nonlinear dynamics for complex linear and optimization problems Luis Vázquez, Salvador Jiménez |
| title_short | Newtonian nonlinear dynamics for complex linear and optimization problems |
| title_sort | newtonian nonlinear dynamics for complex linear and optimization problems |
| topic | Nonlinear mechanics Mathematical optimization System theory Optimierung (DE-588)4043664-0 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Systemtheorie (DE-588)4058812-9 gnd |
| topic_facet | Nonlinear mechanics Mathematical optimization System theory Optimierung Nichtlineare Mechanik Systemtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026243596&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV041257000 |
| work_keys_str_mv | AT vazquezluis newtoniannonlineardynamicsforcomplexlinearandoptimizationproblems AT jimenezsalvador newtoniannonlineardynamicsforcomplexlinearandoptimizationproblems |