Nonnegative matrices, positive operators and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai
World Scientific
[2009]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xvi, 345 Seiten |
| ISBN: | 9789812839176 9812839178 |
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MARC
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| 245 | 1 | 0 | |a Nonnegative matrices, positive operators and applications |c Jiu Ding (The University of Southern Mississippi, USA), Aihui Zhou (Chinese Academy of Sciences, China) |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai |b World Scientific |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a xvi, 345 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Non-negative matrices | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
1.
Elementary Properties of
Nonnegative
Matrices
1
1.1
Algebraic Properties of
Nonnegative
Matrices
....... 1
1.2
Spectral Properties of
Nonnegative
Matrices
........ 4
1.3
Combinatorial Properties of
Nonnegative
Matrices
.... 5
1.4
M-matrices
.......................... 10
1.5
Notes and Remarks
...................... 15
Exercises
........................... 16
2.
The Perron-Frobenius Theory for
Nonnegative
Matrices
19
2.1
Perron s Theorem for Positive Matrices
.......... 19
2.2
Frobenius Theorem for Irreducible
Nonnegative
Matrices
............................ 26
2.3
Ergodic Theorems for
Nonnegative
Matrices
........ 35
2.4
Characterizations of Irreducibility and
Primitivity
.... 40
2.5
Notes and Remarks
...................... 46
Exercises
........................... 47
3.
Stochastic Matrices
51
3.1
Stochastic Matrices
...................... 51
3.2
Doubly Stochastic Matrices
................. 57
3.3
Inequalities Related to Doubly Stochastic Matrices
.... 65
3.4
Ergodic Theorems of Stochastic Matrices
......... 69
3.5
Notes and Remarks
...................... 71
Exercises
........................... 72
ХШ
xiv
Nonnegative
Matrices,
Positive
Operators,
and Applications
4.
Applications of
Nonnegative
Matrices
75
4.1
Finite State Stationary Markov Chains
........... 75
4.2
The Web Information Retrieval
............... 81
4.3
Discrete Dynamical Geometry
................ 85
4.4
Iterative Solutions of Linear Algebraic Equations
..... 90
4.5
Notes and Remarks
...................... 93
Exercises
........................... 94
5.
Fundamental Theory of Positive Operators
97
5.1
Banach Lattices
........................ 98
5.2
Positive Operators
...................... 106
5.3
Ideals and Projections
.................... 114
5.4
L-spaces and ilf-spaces
.................... 118
5.5
Notes and Remarks
...................... 124
Exercises
........................... 125
6.
The Spectral Theory of Positive Operators
127
6.1
The Spectral Theory of Bounded Linear Operators
.... 127
6.2
The Spectral Theory of Positive Operators
......... 137
6.3
Ergodic Theorems of Bounded Linear Operators
..... 142
6.4
Ergodic Theorems of Positive Operators
.......... 146
6.5
Notes and Remarks
...................... 150
Exercises
........................... 152
7.
Markov Operators
155
7.1
Definition and Examples of Markov Operators
...... 155
7.2
Properties of Markov Operators
............... 161
7.3
Ergodic Theorems of Markov Operators
.......... 164
7.4
Asymptotic Periodicity of Markov Operators
....... 168
7.5
Notes and Remarks
...................... 177
Exercises
........................... 178
8.
Frobenius-Perron Operators
181
8.1
Measure-preserving Transformations
............ 181
8.2
Frobenius-Perron Operators
................. 184
8.3
Existence of Absolutely Continuous Invariant Measures
. 191
8.4
Ergodic Properties of Invariant Measures
......... 199
8.5
Notes and Remarks
......................
Contents xv
Exercises
........................... 208
9.
Composition
Operators 211
9.1
Positive Functionals on C(K)
................ 211
9.2
Invariant
Measures of Continuous
Transformations
.... 213
9.3
Ergodic
Theorems of
Composition
Operators
....... 216
9.4
Topological
Transitivity and Ergodicity
.......... 223
9.5
Notes and Remarks
...................... 226
Exercises
........................... 227
10.
Approximations of Markov Operators
229
10.1
Ulam s Piecewise Constant Approximations
........ 230
10.2
Piecewise Linear Markov Approximations
......... 237
10.3
Convergence Rate of Ulam s Method
............ 246
10.4
Convergence Rate of the Markov Method
......... 252
10.5
Notes and Remarks
...................... 259
Exercises
........................... 259
11.
Applications of Positive Operators
261
11.1
Positive Approximations of Continuous Functions
..... 261
11.2
Evolution Differential Equations
.............. 268
11.3
Conformational Molecular Dynamics
............ 272
11.4
Third Generation Wireless Communications
........ 283
11.5
Notes and Remarks
...................... 288
Exercises
........................... 288
Appendix A Foundations of Matrix Theory
291
A.I Basic Concepts and Results
................. 291
A.
2
The Spectral Theory of Matrices
.............. 294
A.3 Analytic Theory of Matrices
................. 301
A.
4
Norms and Convergence
................... 304
Appendix
В
Basic Operator Theory
307
B.I Banach Spaces
........................ 307
B.2 Hilbert Spaces
........................ 313
B.3 Bounded Linear Operators
.................. 315
B.4 Bounded Linear Functionals and Dual Operators
..... 319
xvi
Nonnegative
Matrices,
Positive
Operators,
and Applications
Bibliography
327
Index
333
Nonnegative
matrices and positive operators are widely
applied in science, engineering, and technology. This book
provides the basic theory
ond
several typical modern
science and engineering applications of
nonnegative
matrices and positive operators, including the fundamental
theory, methods, numerical analysis, and applications
in the Google search engine, computational molecub
dynamics, and wireless communications.
Unique
features of this book include
lhe
combiiiaiinn
of the theories
oí
nonneqative man ices and positive
operators as well as the emphasis on applications oi
nonnegative
matrices in the numerical analysis oi
positivt
operators, such as Markov operators and Frobenius-
-Ponan
operators
both
oí
which play key roles in ¡he
sinlisüttii
und
stochastic siudies oi dynamical systems.
It can be used
(¡s g
textbook
loi an
upper level
undergraduate or beginning graduate course in advanced
matrix theory and/or positive
Operators
as
weil
os foi
an advanced topics course in operator theory or ergoiik
theory. In
addition.
її
serves
os a qood
mmm h
researchers in
müítienumcul
sciences, physical
säena*.
eind
Hncjinoering.
|
| any_adam_object | 1 |
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| dewey-ones | 512 - Algebra |
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| id | DE-604.BV036050971 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:10:19Z |
| institution | BVB |
| isbn | 9789812839176 9812839178 |
| language | English |
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| spelling | Ding, Jiu Verfasser (DE-588)138216746 aut Nonnegative matrices, positive operators and applications Jiu Ding (The University of Southern Mississippi, USA), Aihui Zhou (Chinese Academy of Sciences, China) New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai World Scientific [2009] © 2009 xvi, 345 Seiten txt rdacontent n rdamedia nc rdacarrier Non-negative matrices Positive operators Positiver Operator (DE-588)4046876-8 gnd rswk-swf Nichtnegative Matrix (DE-588)4310434-4 gnd rswk-swf Nichtnegative Matrix (DE-588)4310434-4 s Positiver Operator (DE-588)4046876-8 s DE-604 Zhou, Aihui Verfasser (DE-588)123378230 aut 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=018942652&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=018942652&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Ding, Jiu Zhou, Aihui Nonnegative matrices, positive operators and applications Non-negative matrices Positive operators Positiver Operator (DE-588)4046876-8 gnd Nichtnegative Matrix (DE-588)4310434-4 gnd |
| subject_GND | (DE-588)4046876-8 (DE-588)4310434-4 |
| title | Nonnegative matrices, positive operators and applications |
| title_auth | Nonnegative matrices, positive operators and applications |
| title_exact_search | Nonnegative matrices, positive operators and applications |
| title_full | Nonnegative matrices, positive operators and applications Jiu Ding (The University of Southern Mississippi, USA), Aihui Zhou (Chinese Academy of Sciences, China) |
| title_fullStr | Nonnegative matrices, positive operators and applications Jiu Ding (The University of Southern Mississippi, USA), Aihui Zhou (Chinese Academy of Sciences, China) |
| title_full_unstemmed | Nonnegative matrices, positive operators and applications Jiu Ding (The University of Southern Mississippi, USA), Aihui Zhou (Chinese Academy of Sciences, China) |
| title_short | Nonnegative matrices, positive operators and applications |
| title_sort | nonnegative matrices positive operators and applications |
| topic | Non-negative matrices Positive operators Positiver Operator (DE-588)4046876-8 gnd Nichtnegative Matrix (DE-588)4310434-4 gnd |
| topic_facet | Non-negative matrices Positive operators Positiver Operator Nichtnegative Matrix |
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