The joint spectral radius: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schriftenreihe: | Lecture notes in control and information sciences
385 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 144 S. Diagramme |
| ISBN: | 9783540959793 |
Internformat
MARC
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|---|---|---|---|
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| 020 | |a 9783540959793 |9 978-3-540-95979-3 | ||
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| 100 | 1 | |a Jungers, Raphaël |d ca. 20./21. Jh. |e Verfasser |0 (DE-588)1313249750 |4 aut | |
| 245 | 1 | 0 | |a The joint spectral radius |b theory and applications |c Raphaël Jungers |
| 246 | 1 | 3 | |a infinite matrix products, from the joint spectral radius to combinatorics |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XIII, 144 S. |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 385 | |
| 502 | |a Teilw. zugl.: Louvain, Belgium, Univ. Catholique, Diss., 2008 u.d.T.: Infinite matrix products, from the joint spectral radius to combinatorics | ||
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| 830 | 0 | |a Lecture notes in control and information sciences |v 385 |w (DE-604)BV005848579 |9 385 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018333815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018333815 | ||
Datensatz im Suchindex
| _version_ | 1804140304883777536 |
|---|---|
| adam_text | Contents
Introduction
............................
,
.................... 1
Part
I Theory
1
Basics
................................................... 7
1.1
Definitions
............................................ 9
1.2
Basic Results
......................................... 11
1.2.1
Fundamental Theorems
.......................... 12
1.2.2
Basic Properties
................................. 14
1.3
Stability of Dynamical Systems
.......................... 20
1.4
Conclusion
........................................... 22
2
Classical Results and Problems
.......................... 23
2.1
Defectivity and Extremal Norms
........................ 23
2.1.1
Defectivity
..................................... 23
2.1.2
Extremal Norms
................................ 24
2.1.3
Proofs of the Fundamental Theorems
.............. 27
2.2
Complexity
........................................... 28
2.2.1
NP-Hardness
................................... 29
2.2.2
Non Algebraicity
................................ 9,9
2.2.3
Undecidability
.................................. 30
2.2.4
Similar Results for the Joint Spectral
Subradius
..... 31
2.3
Methods of Computation
................, , . ......., . . , . 31
2.3.1
Zero Spectral Radius
............................ 32
2.3.2
Direct
Argumentu
............................... 33
2.3.3
Branch and Bound Methods
...................... 35
2.3.4
Convex Combination Method
..................... 35
2.3.5
A Geometric Algorithm
......................... . 36
2.3.6
Lifting Methods to Improve the Accuracy
.......... 37
XII Contents
2.3.7
Lyapunov Methods
.............................. 38
2.3.8
Similar Results for the Joint Spectral
Subradius
and the Lyapunov Exponent
...................... 43
2.4
The Fmiteness Property
................................ 44
2.5
Conclusion
........................................... 46
3
Nonnegative
Integer Matrices
........................... 47
3.1
Introduction
.......................................... 47
3.2
Auxiliary Facts and Notations
.......................... 49
3.3
Deciding
ρ
< 1
, ρ
— 1,
and
ρ >
1....................... 51
3.4
Deciding Product Boundedness
.......................... 52
3.5
The Rate of Polynomial Growth
......................... 56
3.6
Polynomial Growth for Arbitrary Matrices
................ 59
3.7
Conclusion and Remarks
............................... 61
4
On the Fmiteness Property
ΐον
Rational Matrices
....... 63
4.1
Introduction
.......................................... 63
4.2
Rational vs. Binary Matrices
............................ 64
4.3
The Fitness Property for Pairs of
2
χ
2
Binary Matrices
.... 69
4.4
Conclusion
........................................... 73
Part II Applications
5
Continuity of Wavelet Functions
......................... 77
5.1
From Two-Scale Difference Equations to Matrices
......... 77
5.2
Continuity and Joint Spectral Radius
.................... 80
5.3
Example
............................................. 82
5.4
Conclusion
........................................... 84
6
Capacity of Codes
....................................... 85
6.1
Introduction
.......................................... 85
6.2
Capacity and Joint Spectral Radius
...................... 87
6.3
Upper and Lower Bounds
............................... 90
6.4
Positive Capacity Can Be Decided in Polynomial Time
..... 93
6.5
Positive Capacity Is NP-Hard for Extended Sets
........... 96
6.6
Extremal Norms and Computing the Capacity
............ 98
6.7
Conclusion
........................................... 99
7
Overlap-Free Words
..................................... 101
7.1
Introduction
.......................................... 101
7.2
The Asymptotics of Overlap--Free Words.
.......,......... 104
7.3
Estimation of the Exponents
............................ 108
7.3.1
Estimation of
β
and the Joint Spectral Radius
...... 108
7.3.2
Estimation of a- and the Joint Spectral
Subradius
... 109
7.3.3
Estimation of
σ
and the Lyapunov Exponent
.......
Ill
7.4
Conclusion
........................................... 113
Contents XIII
8 Trackable
Graphs
........................................ 115
8.1
What Is a Trackable Graph?
............................ 115
8.2
How to Recognize a Trackable Graph?
................... 117
8.3
Conclusion and Future Work
............................ 119
Conclusion
.................................................. 121
Part III Appendices
Numerical Values for Overlap-Free Words
................... 127
A.I Numerical Values of Chapter
7.......................... 127
A.2 The Ellipsoidal Norm
.................................. 130
A.3 The Vector
χ
..............,.......................... 131
References
. ,..................................,.............. 133
List of Figures
............................................... 139
Index
............................................,........... 141
|
| any_adam_object | 1 |
| author | Jungers, Raphaël ca. 20./21. Jh |
| author_GND | (DE-588)1313249750 |
| author_facet | Jungers, Raphaël ca. 20./21. Jh |
| author_role | aut |
| author_sort | Jungers, Raphaël ca. 20./21. Jh |
| author_variant | r j rj |
| building | Verbundindex |
| bvnumber | BV024117090 |
| classification_rvk | SI 845 SK 220 SK 620 |
| ctrlnum | (OCoLC)423762815 (DE-599)BVBBV024117090 |
| dewey-full | 515.39 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 512 - Algebra |
| dewey-raw | 515.39 512.5 |
| dewey-search | 515.39 512.5 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| id | DE-604.BV024117090 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:57:51Z |
| institution | BVB |
| isbn | 9783540959793 |
| language | English |
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| physical | XIII, 144 S. Diagramme |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Jungers, Raphaël ca. 20./21. Jh. Verfasser (DE-588)1313249750 aut The joint spectral radius theory and applications Raphaël Jungers infinite matrix products, from the joint spectral radius to combinatorics Berlin [u.a.] Springer 2009 XIII, 144 S. Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 385 Teilw. zugl.: Louvain, Belgium, Univ. Catholique, Diss., 2008 u.d.T.: Infinite matrix products, from the joint spectral radius to combinatorics Spektralradius (DE-588)4182171-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Spektralradius (DE-588)4182171-3 s DE-604 Lecture notes in control and information sciences 385 (DE-604)BV005848579 385 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=018333815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jungers, Raphaël ca. 20./21. Jh The joint spectral radius theory and applications Lecture notes in control and information sciences Spektralradius (DE-588)4182171-3 gnd |
| subject_GND | (DE-588)4182171-3 (DE-588)4113937-9 |
| title | The joint spectral radius theory and applications |
| title_alt | infinite matrix products, from the joint spectral radius to combinatorics |
| title_auth | The joint spectral radius theory and applications |
| title_exact_search | The joint spectral radius theory and applications |
| title_full | The joint spectral radius theory and applications Raphaël Jungers |
| title_fullStr | The joint spectral radius theory and applications Raphaël Jungers |
| title_full_unstemmed | The joint spectral radius theory and applications Raphaël Jungers |
| title_short | The joint spectral radius |
| title_sort | the joint spectral radius theory and applications |
| title_sub | theory and applications |
| topic | Spektralradius (DE-588)4182171-3 gnd |
| topic_facet | Spektralradius Hochschulschrift |
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